Exhibit 5.1

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Keller Rohrback l.l.p.

Thomas A. Sterken

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March 1, 2021

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Ladies and Gentlemen:

We have acted as counsel to Omeros Corporation, a Washington corporation (“Omeros”) in connection with the registration by Omeros under the Securities Act of 1933, as amended (the “Securities Act”), of the offer and sale of shares of common stock of Omeros, par value $0.01 per share, having an aggregate offering price of up to $150.0 million (the “Shares”), pursuant to a Sales Agreement, dated as of March 1, 2021 (the “Sales Agreement”), by and between Omeros and Cantor Fitzgerald & Co. (the “Agent”), pursuant to the registration statement on Form S 3 (File No. 333-235349) filed with the Securities and Exchange Commission (the “Commission”) on December 4, 2019 (the “Registration Statement”). In connection with rendering this opinion, we have reviewed:

(i)the Sale Agreement;

(ii)the Registration Statement; and

(iii)the prospectus dated as of December 4, 2019, as supplemented by the prospectus supplement, dated March 1, 2021, with respect to the offer and sale of the Shares, filed with the Commission on March 1, 2021, pursuant to Rule 424(b) under the Securities Act (the “Prospectus”).

We have reviewed such corporate records, certificates and other documents and such questions of law as we have considered necessary and relevant for the purposes of this opinion. We have assumed that all signatures are genuine, that all documents submitted to us as originals are authentic and that all copies of documents submitted to us conform to the originals.

In rendering this opinion, we have relied as to certain matters on information obtained from public officials, officers of Omeros and other sources we believe to be responsible.

Based upon the foregoing, it is our opinion that the Shares have been duly authorized and, when issued and sold in the manner referred to in the Sales Agreement and upon receipt by Omeros

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in full of payment therefor in accordance with the Sales Agreement, will be validly issued, fully paid and non-assessable.

We are members of the bar of the State of Washington. We do not express any opinion herein on any laws other than the Washington Business Corporation Act, applicable provisions of the Washington State Constitution and reported judicial decisions interpreting these laws.

We hereby consent to the filing of this opinion as Exhibit 5.1 to Omeros’ Current Report on Form 8-K, filed with the Commission on or about March 1, 2021, relating to the offering of the Shares. We also hereby consent to the reference to our name under the heading “Legal Matters” in the Prospectus. In giving such consent, we do not thereby admit that we are in the category of persons whose consent is required under Section 7 of the Securities Act.

Very truly yours,

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/s/ Keller Rohrback L.L.P.

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KELLER ROHRBACK L.L.P.