EX-5.1

Exhibit 5.1

LOGO

Nicole C. Brookshire

+1 617 937 2357

nbrookshire@cooley.com

September 9, 2019

Datadog, Inc.

620 8th Avenue, 45th Floor

New York, New York 10018

Ladies and Gentlemen:

We have acted as counsel to Datadog, Inc., a Delaware corporation (the “Company”), in connection with the filing by the Company of a Registration Statement (No. 333-233428) on Form S-1 (the “Registration Statement”) with the Securities and Exchange Commission, including a related prospectus filed with the Registration Statement (the “Prospectus”), covering an underwritten public offering of up to 27,600,000 shares of the Company’s Class A common stock, par value $0.00001 per share (“Shares”), which includes up to 3,600,000 Shares that may be sold by the Company upon exercise of an option to purchase additional shares to be granted to the underwriters.

In connection with this opinion, we have (i) examined and relied upon (a) the Registration Statement and the Prospectus, (b) the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, each as currently in effect, (c) the forms of the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, filed as Exhibits 3.2 and 3.4 to the Registration Statement, respectively, each of which is to be in effect prior to the closing of the offering contemplated by the Registration Statement and (d) originals or copies certified to our satisfaction of such records, documents, certificates, memoranda and other instruments as in our judgment are necessary or appropriate to enable us to render the opinion expressed below and (ii) assumed that the Shares will be sold at a price established by the Board of Directors of the Company or a duly authorized committee thereof and that the Amended and Restated Certificate of Incorporation referred to in clause (i)(c) is filed with the Secretary of State of the State of Delaware before issuance of the Shares.

We have assumed the genuineness and authenticity of all documents submitted to us as originals, and the conformity to originals of all documents submitted to us as copies and the due execution and delivery by all persons other than by the Company of all documents where due execution and delivery are a prerequisite to the effectiveness thereof. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not sought independently to verify such matters.

Our opinion is expressed only with respect to the General Corporation Law of the State of Delaware. We express no opinion to the extent that any other laws are applicable to the subject matter hereof and express no opinion and provide no assurance as to compliance with any federal or state securities law, rule or regulation.

On the basis of the foregoing, and in reliance thereon, we are of the opinion that the Shares, when sold and issued against payment therefor as described in the Registration Statement and the Prospectus, will be validly issued, fully paid and non-assessable.

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Cooley LLP 500 Boylston Street Boston, MA 02116-3736

t: (617) 937-2300 f: (617) 937-2400 cooley.com