Exhibit 5.1

[Letterhead of Sullivan & Cromwell LLP]

January 22, 2020

CyrusOne LP

CyrusOne Finance Corp.,

2850 N. Harwood Street, Suite 2200,

Dallas, Texas 75201.

Ladies and Gentlemen:

In connection with the registration under the Securities Act of 1933 (the “Act”) of (i) €500,000,000 principal amount of 1.450% Senior Notes due 2027 (the “Securities”) of CyrusOne LP, a Maryland limited partnership, and CyrusOne Finance Corp., a Maryland corporation (each, a “Company”), and (ii) the guarantee (the “Guarantee”) by CyrusOne Inc., a Maryland corporation (the “Guarantor”), we, as your counsel, have examined such corporate records, certificates and other documents, and such questions of law, as we have considered necessary or appropriate for the purposes of this opinion.

Upon the basis of such examination, it is our opinion that (i) assuming the Securities have been duly authorized, executed and delivered by each Company insofar as the laws of the State of Maryland are concerned, the Securities constitute valid and legally binding obligations of each Company and (ii) assuming the Guarantee has been duly authorized, executed and delivered by the Guarantor insofar as the laws of the State of Maryland are concerned, the Guarantee constitutes a valid and legally binding obligation of the Guarantor, in each case, enforceable in accordance with their respective terms, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles.

CyrusOne LP CyrusOne Finance Corp. -2-

In rendering the foregoing opinion, we are expressing no opinion as to Federal or state laws relating to fraudulent transfers and we are not passing upon, and assume no responsibility for, any disclosure in any registration statement or any related prospectus or other offering material relating to the offer and sale of the Securities or the Guarantee.

We note that, as of the date of this opinion, a judgment for money in an action based on the Securities in a Federal or state court in the United States ordinarily would be enforced in the United States only in United States dollars. The date used to determine the rate of conversion of euros into United States dollars will depend upon various factors, including which court renders the judgment. Under Section 27 of the New York Judiciary Law, a state court in the State of New York rendering a judgment on a Security would be required to render such judgment in euros, and such judgment would be converted into United States dollars at the exchange rate prevailing on the date of entry of the judgment.

The foregoing opinion is limited to the Federal laws of the United States and the laws of the State of New York, and we are expressing no opinion as to the effect of the laws of any other jurisdiction. For purposes of our opinion, we have assumed that (i) each Company has been duly formed or incorporated, as applicable, and is an existing limited partnership or corporation, as applicable, under the laws of the State of Maryland, (ii) the Guarantor has been duly incorporated and is an existing corporation under the laws of the State of Maryland, (ii) each of the Indenture and the Third Supplemental Indenture relating to the Securities has been duly authorized, executed and delivered by each Company insofar as the laws of the State of Maryland are concerned and (iv) the Third Supplemental Indenture relating to the Securities has been duly authorized, executed and delivered by the Guarantor insofar as the laws of the State of Maryland are concerned. With respect to all matters of Maryland law, we note that you have received an opinion, dated January 22, 2020, of Venable LLP.

We have relied as to certain factual matters on information obtained from public officials, officers of the Guarantor and other sources believed by us to be responsible, and we have assumed that the Indenture has been duly authorized, executed and delivered by the Trustee thereunder, that the Third Supplemental Indenture relating to the Securities has been duly authorized, executed and delivered by the Trustee and the Paying Agent and Security Registrar thereunder, that the Securities conform to the specimens thereof examined by us, that the Trustee’s certificate of authentication of the Securities has been manually signed by one of the Trustee’s authorized officers, and the signatures on all documents examined by us are genuine, assumptions which we have not independently verified.

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We hereby consent to the filing of this opinion as an exhibit to a Current Report on Form 8-K filed by the Guarantor for purposes of incorporating this opinion into the Registration Statement on Form S-3 relating to the Securities and the Guarantee and to the references to us under the heading “Validity of the Securities” in the prospectus supplement relating to the Securities and the Guarantee. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Act.

Very truly yours,

/s/ SULLIVAN & CROMWELL LLP