POWER OF ATTORNEY

KNOW ALL BY THESE PRESENTS, that the undersigned hereby constitutes and appoints each of Joshua A. Mills, Salini Nandipati, and Chris Visgilio, or each of them singly, to be the undersigned’s true and lawful attorney-in-fact to:

(1)prepare, execute in the undersigned’s name and on the undersigned’s behalf, and submit to the U.S. Securities and Exchange Commission (the “SEC”) a Form ID, including amendments thereto, and any other documents necessary or appropriate to obtain codes and passwords enabling the undersigned to make electronic filings with the SEC of reports required by Section 16(a) of the Securities Exchange Act of 1934 or any rule or regulation of the SEC;

(2)execute for and on behalf of the undersigned, in the undersigned’s capacity as an officer, director and/or stockholder of Digital Realty Trust, Inc. and, in Digital Realty Trust, Inc.’s capacity as general partner of Digital Realty Trust, L.P., Digital Realty Trust, L.P. (together, the “Company”), Forms 3, 4, and 5 and amendments thereto in accordance with Section 16(a) of the Securities Exchange Act of 1934 and the rules thereunder;

(3)do and perform any and all acts for and on behalf of the undersigned which may be necessary or desirable to complete and execute any such Form 3, 4, or 5 and any amendments thereto and timely file such forms with the SEC and any stock exchange or similar authority, including, but not limited to, taking any actions necessary or desirable in connection with effectuating electronic filings; and

(4)take any other action of any type whatsoever which, in the opinion of such attorney-in-fact, may be necessary or desirable in connection with the foregoing authority, it being understood that the documents executed by such attorney-in-fact on behalf of the undersigned pursuant to this Power of Attorney shall be in such form and shall contain such terms and conditions as such attorney-in-fact may approve in such attorney-in-fact’s discretion.

The undersigned hereby grants to each such attorney-in-fact full power and authority to do and perform any and every act and thing whatsoever requisite, necessary, or proper to be done in the exercise of any of the rights and powers herein granted, as fully to all intents and purposes as the undersigned might or could do if personally present, with full power of substitution or revocation, hereby ratifying and confirming all that such attorney-in-fact, or such attorney-in-fact’s substitute or substitutes, shall lawfully do or cause to be done by virtue of this Power of Attorney and the rights and powers herein granted. The undersigned acknowledges that the foregoing attorneys-in-fact, in serving in such capacity at the request of the undersigned, are not assuming, nor is the Company assuming, any of the undersigned’s responsibilities to comply with Section 16 of the Securities Exchange Act of 1934.

This Power of Attorney shall remain in full force and effect until the undersigned is no longer required to file Forms 3, 4, and 5 with respect to the undersigned’s holdings of and transactions in securities issued by the Company, unless earlier revoked by the undersigned in a signed writing delivered to the foregoing attorneys-in-fact. This Power of Attorney may be filed with the SEC as a confirming statement of the authority granted herein.

IN WITNESS WHEREOF, the undersigned has caused this Power of Attorney to be executed as of this 1 day of May, 2015.

Bernard Geoghegan

Digital Realty Trust, Inc. 4