Exhibit 5.1

to Registration Statement

[Letterhead of Jones, Walker, Waechter, Poitevent, Carrère & Denègre, L.L.P.]

March 2, 2012

CenturyLink, Inc.

100 CenturyLink Drive

Monroe, Louisiana 71203

Re: Registration Statement on Form S-3

Ladies and Gentlemen:

We have acted as special counsel to CenturyLink, Inc., a Louisiana corporation (“CenturyLink”), in connection with the preparation of a registration statement on Form S-3 (the “Registration Statement”) filed with the Securities and Exchange Commission (the “Commission”) by CenturyLink and one of its subsidiaries. The Registration Statement relates to the offer and sale by CenturyLink from time to time, pursuant to Rule 415 promulgated under the Securities Act of 1933, as amended (the “Act”), of an indeterminate aggregate initial offering price or number of (i) unsecured senior or subordinated debt securities of CenturyLink (“Debt Securities”), (ii) shares of CenturyLink’s preferred stock (“Preferred Stock”), (iii) depositary shares representing fractional interests in Preferred Stock (“Depositary Shares”), (iv) CenturyLink’s common stock (“Common Stock”), (v) warrants to purchase Debt Securities, Preferred Stock, Depositary Shares, Common Stock, or any combination thereof (“Warrants”) and (vi) units consisting of certain specified securities (the “Units” and, collectively with Debt Securities, Preferred Stock, Depositary Shares, Common Stock and Warrants, the “Securities”), in one or more series as determined by CenturyLink’s Board of Directors, or any committee thereof, in subsequent resolutions (“Subsequent Resolutions”) and as described in the prospectus contained in the Registration Statement (the “Prospectus”) and as to be set forth in one or more supplements to the Prospectus (each such supplement, a “Prospectus Supplement”).

In connection with rendering the opinions expressed below, we have examined originals, or copies certified or otherwise identified to our satisfaction, of such corporate records, certificates of corporate officers and government officials and such other documents as we have deemed necessary or appropriate for the purposes of this opinion, including: (i) the amended and restated Articles of Incorporation of CenturyLink dated as of July 1, 2009, as amended by the Articles of Amendment to the Amended and Restated Articles of Incorporation dated May 20, 2010; (ii) the amended and restated Bylaws of CenturyLink; (iii) the resolutions adopted by the Board of Directors of CenturyLink on January 25, 2012 (the “Board Resolutions”); (iv) the

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indenture (the “Senior Indenture”) dated as of March 31, 1994 between CenturyLink (formerly named Century Telephone Enterprises, Inc.) and Regions Bank (successor to First American Bank & Trust of Louisiana and Regions Bank of Louisiana), as Trustee (the “Trustee”); and (v) such other records of CenturyLink, certificates of CenturyLink’s officers and public officials, and such other documents as we have deemed relevant. As to various questions of fact material to this opinion, we have relied upon representations of officers or directors of CenturyLink and documents furnished to us by CenturyLink without independent verification of their accuracy and upon such other documents, records, certificates and other instruments, including certificates or other written or oral advice of public officials and officers of CenturyLink, as we considered necessary or appropriate in connection with rendering the opinions expressed below.

In our examination of such documents, we have assumed without independent verification (i) that each of the documents and instruments reviewed by us has been duly authorized, executed and delivered by each of the parties thereto other than CenturyLink and is enforceable against such parties in accordance with the terms thereof, (ii) the authenticity of all documents and instruments submitted to us as originals, (iii) the conformity to the originals of all documents and instruments submitted to us as conformed, certified or photostatic copies, (iv) the accuracy and completeness of all corporate records made available to us by CenturyLink and its subsidiaries, (v) the absence of any other documents, instruments, records, agreements or understandings that alter, modify or change the validity or accuracy of the representations made to us orally or as set forth in any documents, instruments, records or agreements provided to or reviewed by us, (vi) the genuineness of all signatures on all documents and instruments examined by us, and (vii) the power and legal capacity of all persons (other than CenturyLink and its subsidiaries) who have executed documents reviewed by us hereunder.

Based upon the foregoing and subject to the following qualifications and comments, we are of the opinion that:

1. CenturyLink is a corporation duly organized, validly existing and in good standing under the laws of the State of Louisiana and has all requisite corporate power to issue the Securities.

2. Each series of senior Debt Securities issued under the Senior Indenture will be legally issued and binding obligations of CenturyLink when (i) the Registration Statement shall have become effective under the Act, (ii) any necessary supplemental indenture to the Senior Indenture shall have been duly authorized, executed and delivered by CenturyLink and the Trustee, (iii) the terms of such series of Debt Securities shall have been established and approved in accordance with a supplemental indenture or Subsequent Resolutions, as contemplated by the Senior Indenture and the Registration Statement, (iv) a Prospectus Supplement with respect to such series of Debt Securities shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act and (v) any required certificates representing such series of Debt Securities shall have been duly authenticated, executed and delivered in accordance with the Senior Indenture, and such Securities shall have been duly delivered to, or registered in the name of, the purchasers thereof or a depositary acting on their behalf against payment of the agreed consideration therefor in accordance with the applicable underwriting, purchase or similar agreement.

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3. Each series of subordinated Debt Securities will be legally issued and binding obligations of CenturyLink when (i) the Registration Statement shall have become effective under the Act, (ii) a subordinate indenture is entered into between CenturyLink and a bank or trust company, as trustee, pursuant to which such series of subordinated debt securities are to be issued (the “Subordinated Indenture” and, collectively with the Senior Indenture, the “Indentures”), and any necessary supplemental indenture to such Subordinated Indenture shall have been duly authorized, executed and delivered by CenturyLink and the trustee thereunder, (iii) such Subordinated Indenture and trustee have been qualified under the Trust Indenture Act of 1939, as amended (the “Trust Indenture Act”) and a Form T-1 has been properly filed with the Commission, (iv) the terms of such series of Debt Securities shall have been established and approved in accordance with the terms and conditions of such Subordinated Indenture, as contemplated by the Registration Statement, (v) a Prospectus Supplement with respect to such series of Debt Securities shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act and (vi) any required certificates representing such series of Debt Securities shall have been duly authenticated, executed and delivered in accordance with such Subordinated Indenture, and such Securities shall have been duly delivered to, or registered in the name of, the purchasers thereof or a depositary acting on their behalf against payment of the agreed consideration therefor in accordance with the applicable underwriting, purchase or similar agreement.

4. Each series of Preferred Stock will be legally issued, fully paid and non-assessable when (i) the Registration Statement shall have become effective under the Act, (ii) the terms of such series of Preferred Stock shall have been established and approved, in conformity with applicable law, in accordance with Subsequent Resolutions, as contemplated by the Registration Statement, (iii) Articles of Amendment setting forth the terms of such series of Preferred Stock shall have been duly executed, acknowledged, filed and recorded and shall have become effective in accordance with the Louisiana Business Corporation Law (“LBCL”), (iv) a Prospectus Supplement with respect to such series of Preferred Stock shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act and (v) any required certificates representing such series of Preferred Stock shall have been duly executed, countersigned and registered, and duly delivered to the purchasers thereof or a depositary acting on their behalf against payment of the agreed consideration therefor (but not less than par value) in accordance with the applicable underwriting, purchase or similar agreement.

5. Each series of Depositary Shares will be legally issued, fully paid and non-assessable when (i) the Registration Statement shall have become effective under the Act, (ii) the terms of such series of Depositary Shares, including the adoption of the Articles of Amendment setting forth the terms of the Preferred Stock underlying such series of Depositary Shares, shall have been established and approved, in conformity with applicable law, in accordance with Subsequent Resolutions, as contemplated by the Registration Statement, (iii) the depositary agreement or agreements relating to the Depositary Shares and the related depositary receipts shall have been duly established and approved, and the depositary appointed by CenturyLink, in

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accordance with Subsequent Resolutions, (iv) a Prospectus Supplement with respect to such series of Depositary Shares shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act, (v) the shares of Preferred Stock underlying such series of Depositary Shares have been deposited with a bank or trust company under the depositary agreement, and (vi) any required depositary receipts representing such series of Depositary Shares have been duly executed, countersigned and registered, and duly delivered in accordance with the depositary agreement approved by the Subsequent Resolutions against payment of the agreed consideration therefor.

6. The Common Stock will be legally issued, fully paid and non-assessable when (i) the Registration Statement shall have become effective under the Act, (ii) the issuance and sale of the Common Stock shall have been approved, in conformity with applicable law, in accordance with Subsequent Resolutions, as contemplated by the Registration Statement, (iii) a Prospectus Supplement with respect to such shares of Common Stock shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act and (iv) any required certificates representing the Common Stock shall have been duly executed, countersigned and registered and duly delivered to the purchasers thereof or a depositary acting on their behalf against payment of the agreed consideration therefor (but not less than the par value) in accordance with the applicable underwriting, purchase or similar agreement.

7. Each series of Warrants to purchase Debt Securities, Preferred Stock, Depositary Shares or Common Stock will be legally issued and binding obligations of CenturyLink when (i) the Registration Statement shall have become effective under the Act, (ii) a warrant agreement relating to such Warrants shall have been duly authorized, executed and delivered by CenturyLink and the warrant agent or agents thereunder, (iii) the terms of such Warrants and the Securities issuable upon exercise thereof shall have been established and approved in accordance with Subsequent Resolutions (or a supplemental indenture to the applicable Indenture), as contemplated by the Registration Statement, the warrant agreement relating to such Warrants and, as applicable, the Senior Indenture, the Subordinated Indenture, the LBCL or any other governing instrument or laws, (iv) a Prospectus Supplement with respect to such Warrants shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act, (v) any and all actions required under the applicable Indenture to validly issue any Debt Securities upon exercise of the Warrants, any and all action required under the LBCL to validly issue any Preferred Stock or Common Stock upon exercise of the Warrants, or any and all comparable actions under the governing instruments to validly issue any other Securities upon exercise of the Warrants, shall have been duly taken, (vi) any required qualifications under the Trust Indenture Act shall have been received and (vii) any instruments evidencing such Warrants shall have been duly executed and authenticated or countersigned as provided in the warrant agreement relating thereto and duly delivered to the purchasers thereof or a depositary acting on their behalf against payment of the agreed consideration therefor in accordance with the applicable underwriting, purchase or similar agreement.

8. The Units will be legally issued, fully paid and non-assessable when (i) the Registration Statement shall have become effective under the Act, (ii) the Units, and one or more unit agreements (each, a “Unit Agreement”) among CenturyLink, one or more banks or trust

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companies, as unit agent (each, “Unit Agent”), and the holders from time to time of the Units, and any necessary accompanying documentation, shall have been duly authorized, executed and delivered by CenturyLink and each other party thereto, (iii) the terms of the Units and the Unit Agreement shall have been established and approved in accordance with Subsequent Resolutions, as contemplated by the Registration Statement, and, as applicable, the Senior Indenture, the Supplemental Indenture, the LBCL or any other governing instrument or laws, (iv) a Prospectus Supplement with respect to such Units shall have been filed (or transmitted for filing) with the Commission pursuant to Rule 424(b) of the Act, (v) any and all actions required under the applicable Indenture to validly issue any Debt Securities pursuant to the Units, any and all actions required under the LBCL to validly issue any Preferred Stock or Common Stock pursuant to the Units, or any and all comparable actions under the governing instruments to validly issue any other Securities pursuant to the Units, shall have been taken, (vi) any required qualifications under the Trust Indenture Act shall have been received and (vii) any required certificates or similar documentation representing the Units shall have been duly executed, countersigned and registered and duly delivered to the purchasers thereof or a depositary acting on their behalf against payment of the agreed consideration therefor in accordance with the applicable underwriting, purchase or similar agreement.

In connection with our opinions expressed above, we have assumed that, at or prior to the time of the delivery of any such Security: (i) the Board of Directors, or any committee thereof, of CenturyLink shall have duly and validly taken all corporate action necessary to authorize the issuance and sale of each such Security pursuant to the adoption of Subsequent Resolutions (including the due reservation of Securities issuable upon the conversion, exercise or exchange of any other Security) and such authorization shall not have been modified or rescinded; (ii) the Registration Statement and any supplements and amendments thereto (including post-effective amendments) shall have been automatically effective upon filing and such effectiveness shall not have been terminated or rescinded; (iii) the Registration Statement will comply with all applicable laws at all times during which the Securities are offered and issued as contemplated by the Registration Statement, and CenturyLink shall continue to remain eligible to use such Registration Statement; (iv) the applicable Prospectus Supplement filed with the Commission describing the Securities offered thereby will comply with all applicable laws; (v) all Securities will be issued and sold in compliance with all applicable federal and state securities laws and in the manner stated in the Registration Statement and the appropriate Prospectus Supplement; (vi) the definitive purchase, underwriting or similar agreement and any other necessary agreement with respect to any Securities offered or issued will have been duly authorized and validly executed and delivered by CenturyLink and the other parties thereto; (vii) the Senior Indenture and the Subordinated Indenture have been duly authorized, executed and delivered by CenturyLink and the applicable trustees, and each indenture and the applicable trustees have been and continues to be qualified under the Trust Indenture Act; (viii) all Securities will be issued in accordance with the terms and conditions of the Subsequent Resolutions authorizing the issuance of such Securities and (ix) there will not have occurred any change in law affecting the validity or enforceability of any such Security. We have also assumed that none of the terms of any Security to be established subsequent to the date hereof nor the issuance and delivery of such Security, nor the compliance by CenturyLink with the terms of such Security, will violate

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any applicable law or regulation (including those relating to the regulation of communications companies) or will result in a violation of any provision of any instrument or agreement then binding upon CenturyLink, or any restriction imposed by any court or governmental body having jurisdiction over CenturyLink or its assets.

Our opinions expressed above regarding the enforceability of certain of CenturyLink’s obligations are subject to the qualification that enforceability may be limited by (i) applicable bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium or similar laws of general applicability relating to or affecting the enforcement of creditors’ rights, (ii) general principles of equity (regardless of whether enforceability is considered in a proceeding in equity or at law), (iii) public policy considerations that may limit the rights of parties to obtain certain remedies and (iv) governmental authority to limit, delay or prohibit the making of payments outside of the United States or in a foreign currency or currency unit.

We do not express any opinion herein concerning any law other than the LBCL (including the statutory provisions and reported judicial decisions interpreting the foregoing). We express no opinion as to the application of the securities or blue sky laws of the various states to the sale of any Securities.

This letter has been furnished in accordance with the requirements of Item 16 of Form S-3 and Item 601(b)(5)(i) of Regulation S-K promulgated by the Commission, and is expressly limited to the specific issues addressed herein. We render no opinion, whether by implication or otherwise, as to any other matter relating to CenturyLink, the Registration Statement, the Securities or any of the transactions contemplated or discussed thereunder. This letter speaks only as of the date hereof. We assume no obligation to revise or supplement this letter should the presently applicable laws be changed by legislative action, judicial decision or otherwise.

We consent to the filing of this letter as an exhibit to the Registration Statement and to the reference to us in the Prospectus under the caption “Legal Matters.” In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Act or the general rules and regulations of the Commission.

Very truly yours,

/s/ Jones, Walker, Waechter, Poitevent,

     Carrère & Denègre, L.L.P.

Jones, Walker, Waechter, Poitevent,

Carrère & Denègre, L.L.P.