Exhibit 5.1

December 17, 2018

Western Gas Equity Partners, LP

1201 Lake Robbins Drive

The Woodlands, Texas 77380-1046

Ladies and Gentlemen:

We are acting as counsel for Western Gas Equity Partners, LP, a Delaware limited partnership (the “Partnership”), in connection with the preparation of the Registration Statement on Form S-4 (the “Registration Statement”) initially filed on the date hereof with the United States Securities and Exchange Commission (the “Commission”) in connection with the registration by the Partnership under the Securities Act of 1933, as amended (the “Securities Act”), of the offer and issuance by the Partnership of up to an aggregate of 234,150,770 of its common units representing limited partner interests in the Partnership (the “Common Units”), pursuant to a Contribution Agreement and Agreement and Plan of Merger, dated as of November 7, 2018 (the “Merger Agreement”), by and among Anadarko Petroleum Corporation, Anadarko E&P Onshore LLC, APC Midstream Holdings, LLC, the Partnership, Western Gas Equity Holdings, LLC (the “General Partner”), Western Gas Partners, LP, Western Gas Holdings, LLC, Clarity Merger Sub, LLC, WGR Asset Holding Company LLC, WGR Operating, LP, Kerr-McGee Gathering LLC, Kerr-McGee Worldwide Corporation and Delaware Basin Midstream, LLC. We have also participated in the preparation of the proxy statement/prospectus (the “Proxy Statement/Prospectus”) contained in the Registration Statement to which this opinion is an exhibit.

In connection with the rendering of the opinion hereinafter set forth, we have examined (i) executed copies of the organizational documents of the Partnership and the General Partner, (ii) the Registration Statement, including the Proxy Statement/Prospectus, (iii) resolutions of the Board of Directors of the General Partner, (iv) the Merger Agreement and (v) such other certificates, statutes and other instruments and documents as we considered appropriate for purposes of the opinions hereafter expressed. In addition, we reviewed such questions of law as we considered appropriate.

In connection with rendering the opinion set forth below, we have assumed that (i) all information contained in all documents reviewed by us is true and correct, (ii) all signatures on all documents examined by us are genuine, (iii) all documents submitted to us as originals are authentic and complete and all documents submitted to us as copies conform to the originals of those documents, (iv) the Registration Statement, and any amendments thereto (including post-effective amendments), will be effective and comply with all applicable laws and (v) all Common Units will be issued and delivered in accordance with the terms of the Merger Agreement and in the manner specified in the Registration Statement.

Vinson & Elkins LLP Attorneys at Law Austin Beijing Dallas Dubai Hong Kong Houston London Moscow New York Palo Alto Richmond Riyadh San Francisco Taipei Tokyo Washington 1001 Fannin Street, Suite 2500 Houston, TX 77002-6760 Tel +1.713.758.2222 Fax +1.713.758.2346 velaw.com

December 17, 2018 Page 2

Based on the foregoing, and subject to the assumptions, qualifications, limitations and exceptions set forth herein, we are of the opinion that, when issued and delivered in accordance with the terms of the Merger Agreement, the Common Units will be validly issued, fully paid (to the extent required under the First Amended and Restated Agreement of Limited Partnership of the Partnership) and non-assessable (except as such non-assessability may be affected by Section 17-303, 17-607 or 17-804 of the Delaware Revised Uniform Limited Partnership Act (the “DRULPA”) and as described in the Proxy Statement/Prospectus).

The foregoing opinion is limited to the DRULPA (including the applicable provisions of the Delaware Constitution and the reported judicial decisions interpreting these laws) and the federal laws of the United States of America. We are expressing no opinion as to the effect of the laws of any other jurisdiction, domestic or foreign.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to the use of our name in the Proxy Statement/Prospectus forming a part of the Registration Statement 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 Securities Act.

Very truly yours,

/s/ Vinson & Elkins L.L.P.

Vinson & Elkins L.L.P.