Odyssey Marine Exploration (OMEX) 8-K Entry into a Material Definitive Agreement

Exhibit 5.1

Akerman LLP 401 E. Jackson Street Suite 1700 Tampa, FL 33602-5250   T: 813 223 7333 F: 813 223 2837

November 2, 2018

Odyssey Marine Exploration, Inc.

5215 W. Laurel Street

Tampa, Florida 33607

Re: Odyssey Marine Exploration, Inc.

Ladies and Gentlemen:

Reference is made to our opinion letter dated October 2, 2018, and included in the Registration Statement on FormS-3 (RegistrationNo. 333-227666) filed with the Securities and Exchange Commission (the “Commission”) on October 2, 2018, together with Amendment No. 1 to Registration Statement on FormS-3 filed with the Commission on October 17, 2018 (together, the “Registration Statement”), by Odyssey Marine Exploration, Inc. (the “Company”) pursuant to the requirements of the Securities Act of 1933, as amended (the “Act”).

We are rendering this supplemental opinion in connection with the prospectus supplement (the “Prospectus Supplement”) dated October 31, 2018. The Prospectus Supplement relates to the offering by the Company of (i) up to 700,000 shares (the “Shares”) of the Company’s common stock, par value $0.001 per share (the “Common Stock”), (ii) common stock purchase warrants (the “Warrants”) to purchase up to an additional 700,000 shares of the Common Stock (the “Warrant Shares” and, together with the Shares, the “Securities”), and (iii) the issuance of the Warrant Shares upon the exercise of the Warrants. We understand that the Securities are to be offered and sold in the manner set forth in the Registration Statement and the Prospectus Supplement.

This opinion letter is being furnished in accordance with the requirements of Item 601(e)(i) of RegulationS-K under the Act. This opinion letter is limited to the matters expressly stated herein, and no opinions are to be inferred or implied beyond the opinions expressly so stated.

We have acted as your counsel in connection with the preparation of the Registration Statement and the Prospectus Supplement. In connection with this opinion letter, we have examined the Registration Statement, including the Prospectus contained therein (the “Prospectus”), the Prospectus Supplement, the form of Common Stock Purchase Warrant (the “Warrant Agreement”) to be issued to investors at the closing of the offering, and the Securities Purchase Agreement (the “SPA”) that are exhibits to the Company’s Current Report on Form8-K dated November 2, 2018, and such corporate records, documents, instruments and certificates of

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public officials and of the Company that we have deemed necessary for the purpose of rendering the opinions set forth herein. We have also reviewed such matters of law as we considered necessary or appropriate as a basis for the opinion set forth below.

With your permission, we have made and relied upon the following assumptions, without any investigation or inquiry by us, and our opinion expressed below is subject to, and limited and qualified by the effect of, such assumptions: (i) all corporate records furnished to us by the Company are accurate and complete; (ii) the Registration Statement, the Prospectus Supplement, the Warrant Agreement, and the SPA filed by the Company with the Commission are identical to the forms of the documents that we have reviewed; (iii) all statements as to factual matters that are contained in the Registration Statement (including the exhibits to the Registration Statement) and the Prospectus Supplement are accurate and complete; (iv) the Company will sell and issue the Securities in accordance with the manner described in the Prospectus Supplement and the SPA; and (v) with respect to documents that we reviewed in connection with this opinion letter, all documents submitted to us as certified, facsimile or photostatic copies conform to the originals of such documents, all such original documents are authentic, the signatures on all documents are genuine, and all natural persons who have executed any of the documents have the legal capacity to do so.

Based on the foregoing, and subject to the further assumptions and qualifications set forth below, it is our opinion that when (i) each of the Warrant Agreements have been executed and delivered by the Company, and (ii) the Warrant Agreements have been offered and sold in accordance with the terms of the Prospectus Supplement and the SPA, each of the Warrant Agreements will be a valid and binding obligation of the Company, enforceable against the Company in accordance with their terms. Notwithstanding the foregoing, our opinion that the Warrant Agreements will be a valid and binding obligation of the Company, enforceable against the Company in accordance with their terms are subject to the following assumptions: (i) limitations imposed by bankruptcy, insolvency, reorganization, arrangement, fraudulent conveyance, moratorium or other laws relating to or affecting the rights of creditors generally; (ii) rights to indemnification and contribution, which may be limited by applicable law or equitable principles; and (iii) general principles of equity, including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing, and the possible unavailability of specific performance or injunctive relief and limitation of rights of acceleration, regardless of whether such enforceability is considered a proceeding in equity or law.

We express no opinion as to matters governed by laws of any jurisdiction other than the State of New York. We neither express nor imply any obligation with respect to any other laws or the laws of any other jurisdiction or of the United States. For purposes of this opinion, we assume that the Securities will be issued in compliance with all applicable state securities or blue sky laws.

With respect to our opinion, we have, without any investigation on our part, assumed the accuracy of, and to the extent necessary in connection with the opinion contained herein, relied upon the opinion dated as of the date hereof furnished to you by Snell & Wilmer, as to Nevada

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law, and our opinion regarding the Company is subject to the same qualifications and limitations with respect to matters of Nevada law as are expressed in such opinion letter.

We assume no obligation to update or supplement this opinion letter if any applicable laws change after the date of this opinion letter or if we become aware after the date of this opinion letter of any facts, whether existing before or arising after the date hereof, that might change the opinions expressed above. Without limiting the generality of the foregoing, we neither express nor imply any opinion regarding the contents of the Registration Statement or the Prospectus Supplement, other than as expressly stated herein with respect to the Warrant Agreements.

This opinion letter is furnished in connection with the filing of the Prospectus Supplement and may not be relied upon for any other purpose without our prior written consent in each instance. Further, no portion of this letter may be quoted, circulated or referred to in any other document for any other purpose without our prior written consent.

We hereby consent to the use of our name under the heading “Legal Matters” in the Prospectus Supplement filed by the Company with the Commission. We further consent to the filing of this opinion letter with the Commission in connection with the filing of the Prospectus Supplement referred to above. In giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Act or the rules and regulations of the Commission issued thereunder.

Sincerely,

/s/ Akerman LLP

AKERMAN LLP