Exhibit 5.1

Hogan Lovells US LLP Columbia Square 555 Thirteenth Street, NW Washington, DC 20004 T +1 202 637 5600 F +1 202 637 5910 www.hoganlovells.com

June 4, 2020

Board of Directors

QTS Realty Trust, Inc.

12851 Foster Street

Overland Park, KS 66213

Ladies and Gentlemen:

We are acting as counsel to QTS Realty Trust, Inc., a Maryland corporation (the “Company”), in connection with the public offering of up to 5,060,000 shares of Class A common stock, par value $0.01 per share, of the Company (the “Common Stock”) by the Company (including up to 660,000 shares of Common Stock being purchased by the underwriters of the public offering pursuant to their option to purchase such shares of Common Stock) (the “Shares”) pursuant to (i) the terms of the Underwriting Agreement dated June 1, 2020, by and among the Company, QualityTech, LP, a Delaware limited partnership (the “Operating Partnership”), and BofA Securities, Inc., Morgan Stanley & Co. LLC, Goldman Sachs & Co. LLC, Jefferies LLC, and J.P. Morgan Securities LLC, as representatives of the several underwriters named on Schedule A thereto, and BofA Securities, Inc. and Morgan Stanley & Co. LLC, as forward sellers and Bank of America, N.A. and Morgan Stanley & Co. LLC as forward purchasers (the “Underwriting Agreement”), and (ii) the letter agreements each dated June 1, 2020 (the “Forward Sale Agreements”), by and between the Company and each of Bank of America, N.A. and Morgan Stanley & Co. LLC, in their capacity as forward purchasers. The offering of the Shares by the Company is being made pursuant to a prospectus supplement dated June 1, 2020 and the accompanying base prospectus dated April 17, 2019 (such documents, collectively, the “Prospectus”) that form part of the Company’s effective registration statement on Form S-3 (File No. 333-230923) (the “Registration Statement”). This opinion letter is furnished to you at your request to enable you to fulfill the requirements of Item 601(b)(5) of Regulation S-K, 17 C.F.R. § 229.601(b)(5), in connection with the Registration Statement.

For purposes of this opinion letter, we have examined copies of such agreements, instruments and documents as we have deemed an appropriate basis on which to render the opinion hereinafter expressed. In our examination of the aforesaid documents, we have assumed the genuineness of all signatures, the legal capacity of all natural persons, the accuracy and completeness of all documents submitted to us, the authenticity of all original documents, and the conformity to authentic original documents of all documents submitted to us as copies (including telecopies). We also have assumed that the Shares will not be issued in violation of the ownership limit contained in the Company’s Articles of Amendment and Restatement. As to all matters of fact, we have relied on the representations and statements of fact made in the documents so reviewed, and we have not independently established the facts so relied on. This opinion letter is given, and all statements herein are made, in the context of the foregoing.

This opinion letter is based as to matters of law solely on the applicable provisions of Maryland General Corporation Law, as amended. We express no opinion herein as to any other laws, statutes, ordinances, rules or regulations.

Based upon, subject to and limited by the foregoing, we are of the opinion that following (i) issuance and delivery of the Shares pursuant to the terms of (a) the Underwriting Agreement and (b) the Forward Sale Agreements, and (ii) receipt by the Company pursuant thereto of the consideration for the Shares specified in the resolutions of the Board of Directors of the Company and the Pricing Committee of the Board of Directors, the Shares will be validly issued, fully paid and nonassessable.

This opinion letter has been prepared for use in connection with the filing by the Company of a Current Report on Form 8-K on the date hereof relating to the offer and sale of the Shares, which Form 8-K will be incorporated by reference into the Registration Statement and Prospectus, and speaks as of the date hereof. We assume no obligation to advise you of any changes in the foregoing subsequent to the delivery of this letter.

We hereby consent to the filing of this opinion letter as Exhibit 5.1 to the above-described Form 8-K and to the reference to this firm under the caption “Legal Matters” in the Prospectus. In giving this consent, we do not thereby admit that we are an “expert” within the meaning of the Securities Act of 1933, as amended.

Very truly yours,

/s/ Hogan Lovells US LLP

HOGAN LOVELLS US LLP