Exhibit 3.1

FIRST AMENDMENT

TO

THIRTEENTH AMENDED AND RESTATED

AGREEMENT OF LIMITED PARTNERSHIP

OF

DIGITAL REALTY TRUST, L.P.

THIS FIRST AMENDMENT TO THIRTEENTH AMENDED AND RESTATED AGREEMENT OF LIMITED PARTNERSHIP of Digital Realty Trust, L.P., dated as of April 7, 2014 (this “First Amendment”), is entered into by and among Digital Realty Trust, Inc., a Maryland corporation (the “Company”), as the General Partner and the Persons whose names are set forth on Exhibit A attached hereto, as the Limited Partners, together with any other Persons who become Partners in the Partnership as provided in the Partnership Agreement (as defined below).

WHEREAS, the General Partner and the Limited Partners have entered into that certain Thirteenth Amended and Restated Agreement of Limited Partnership of Digital Realty Trust, L.P., dated as of March 26, 2014 (the “Partnership Agreement”);

WHEREAS, pursuant to Sections 7.3.C(2) and 7.3.C(3) thereof, the Partnership Agreement may be amended by the General Partner to reflect the issuance of additional Partnership Interests pursuant to Sections 4.3, 4.4, 4.5, 5.4 and 6.2.B thereof and to set forth or amend the designations, rights, powers, duties and preferences of the holders of any additional Partnership Interests issued pursuant to Article 4 thereof; and

WHEREAS, the General Partner and the Partnership believe it is desirable and in the best interest of the Partnership to amend the Partnership Agreement as set forth herein.

NOW, THEREFORE, pursuant to Sections 2.4, 7.3.C(2) and 7.3.C(3) of the Partnership Agreement, the General Partner, on its own behalf and as attorney-in-fact for the Limited Partners, hereby amends the Partnership Agreement as follows::

SECTION 1. Defined Terms. Capitalized terms used but not defined herein shall have the meanings assigned to such terms in the Partnership Agreement.

SECTION 2. Amendment of the Partnership Agreement. The Partnership Agreement is hereby amended as follows:

(a) The defined term “Series H Articles Supplementary” contained in Section 1.1 of the Partnership Agreement is hereby amended and restated in its entirety as follows:

“Series H Articles Supplementary” means (i) the Articles Supplementary of the General Partner in connection with its REIT Series H Preferred Shares, as filed with the Maryland State Department of Assessments and Taxation on March 25, 2014, as corrected by the Certificate of Correction filed with, and accepted for record by, the Maryland State Department

of Assessments and Taxation on April 4, 2014 and (ii) the Articles Supplementary of the General Partner in connection with its REIT Series H Preferred Shares, as filed with the Maryland State Department of Assessments and Taxation on April 4, 2014.”

(b) The last sentence in Section 24.1 of the Partnership Agreement is hereby amended and restated in its entirety as follows:

“The number of Series H Preferred Units shall be 15,800,000.”

(c) Exhibit A of the Partnership Agreement is hereby amended and restated in its entirety by the Exhibit A attached hereto.

SECTION 3. Miscellaneous.

(a) Effect of Amendment. Except as specifically modified hereby, all terms and provisions of the Partnership Agreement shall continue to remain in full force and effect. Each reference in the Partnership Agreement to “this Agreement,” “hereunder,” “hereof,” “herein” or words of like import shall mean and be a reference to the Partnership Agreement as amended hereby, and this First Amendment and the Partnership Agreement shall be read together and construed as a single instrument.

(b) Counterparts. This First Amendment may be executed in two or more counterparts, each of which when and as executed shall be deemed to be an original, and all of which when taken together shall constitute one and the same instrument.

(c) Binding Effect. This First Amendment shall be binding upon and inure to the benefit of the parties hereto and their heirs, executors, administrators, successors, legal representatives and permitted assigns.

(d) Headings. The headings in this First Amendment are for convenience of reference only and shall not limit or otherwise affect the meaning hereof.

(e) Applicable Law. This First Amendment shall be construed in accordance with and governed by the laws of the State of Maryland, without regard to the principles of conflicts of law.

(f) Invalidity of Provisions. If any provision of this First Amendment is or becomes invalid, illegal or unenforceable in any respect, the validity, legality and enforceability of the remaining provisions contained herein shall not be affected thereby.

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IN WITNESS WHEREOF, the undersigned has executed this Amendment to the Thirteenth Amended and Restated Agreement of Limited Partnership as of the date first written above.

Signature Page to Amendment to Thirteenth Amended and Restated Agreement of

Limited Partnership of Digital Realty Trust, L.P.

S-1

EXHIBIT A

(Dated April 7, 2014)

PARTNERS, CONTRIBUTIONS AND PARTNERSHIP INTERESTS

Common or Profits Interest Units:

Class C Unit Holders

Class D Unit Holders

Series E Preferred Units: