EXHIBIT 5.1

Opinion of Cooley LLP

[Cooley Letterhead]

Chadwick L. Mills
+1 650 843 5654
cmills@cooley.com

May 26, 2020

Geron Corporation
919 East Hillsdale Boulevard, Suite 250
Foster City, California 94404

Ladies and Gentlemen:

You have requested our opinion, as counsel to Geron Corporation, a Delaware corporation (the “Company”), in connection with the offering by the Company of (i) up to 107,049,375 shares of its common stock (the “Common Stock”), par value $0.001 (the “Shares”) (ii) pre-funded warrants (the “Pre-Funded Warrants”) to purchase up to 8,335,239 shares of Common Stock (the “Pre-Funded Warrant Shares”), in each case, together with accompanying warrants (together with the Pre-Funded Warrants, the ”Warrants”) to purchase up to 57,692,307 shares of Common Stock (together with the Pre-Funded Warrant Shares, the “Warrant Shares”), pursuant to a Registration Statement on Form S-3 (No. 333-225184) (the “Initial Registration Statement”), filed with the Securities and Exchange Commission (the “Commission”) under the Securities Act of 1933, as amended (the “Act”), a Registration Statement on Form S-3 (No. 333-238595), filed with the Commission pursuant to Rule 462(b) under the Act (together with the Initial Registration Statement, the “Registration Statement”), the prospectus included in the Initial Registration Statement (the “Base Prospectus”), and the prospectus supplement, dated May 21, 2020, and filed with the Commission pursuant to Rule 424(b) under the Act (together with the Base Prospectus, the “Prospectus”).

In connection with this opinion, we have examined and relied upon the Registration Statement, the Prospectus, the form of Warrant, the Company’s Amended and Restated Certificate of Incorporation and Amended and Restated Bylaws, each as currently in effect, and 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. We have assumed the genuineness of all signatures, the authenticity of all documents submitted to us as originals, the conformity to originals of all documents submitted to us as copies; the accuracy, completeness and authenticity of certificates of public officials, and the due authorization, execution and delivery of all documents by all persons other than the Company where authorization, execution and delivery are prerequisites to the effectiveness of such documents. As to certain factual matters, we have relied upon a certificate of an officer of the Company and have not independently verified such matters.

With regard to our opinion regarding the Warrant Shares, we express no opinion to the extent that, notwithstanding its current reservation of shares of Common Stock, future issuances of securities, including the Warrant Shares, of the Company and/or antidilution adjustments to outstanding securities of the Company, including the Warrants, cause the Warrants to be exercisable for more shares of Common Stock than the number that then remain authorized but unissued. Further, we have assumed the Exercise Price (as defined in the Warrants) will not be adjusted to an amount below the par value per share of the Common Stock.

COOLEY LLP   101 CALIFORNIA STREET, 5^TH FLOOR, CA   94111-5800
T: (415) 693-2000  F: (415) 693-2222  COOLEY.COM

Geron Corporation
May 26, 2020
Page Two

With regard to our opinion concerning the Warrants constituting valid and binding obligations of the Company:

(i) Our opinion is subject to, and may be limited by, (a) applicable bankruptcy, reorganization, insolvency, moratorium, fraudulent conveyance, debtor and creditor, and similar laws which relate to or affect creditors’ rights generally, and (b) general principles of equity (including, without limitation, concepts of materiality, reasonableness, good faith and fair dealing) regardless of whether considered in a proceeding in equity or at law.

(ii) Our opinion is subject to the qualification that the availability of specific performance, an injunction or other equitable remedies is subject to the discretion of the court before which the request is brought.

(iii) We express no opinion as to any provision of the Warrants that: (a) provides for liquidated damages, buy-in damages, monetary penalties, prepayment or make-whole payments or other economic remedies to the extent such provisions may constitute unlawful penalties, (b) relates to advance waivers of claims, defenses, rights granted by law, or notice, opportunity for hearing, evidentiary requirements, statutes of limitations, trial by jury, or procedural rights, (c) restricts non-written modifications and waivers, (d) provides for the payment of legal and other professional fees where such payment is contrary to law or public policy, (e) relates to exclusivity, election or accumulation of rights or remedies, (f) authorizes or validates conclusive or discretionary determinations, or (g) provides that provisions of the Warrants are severable to the extent an essential part of the agreed exchange is determined to be invalid and unenforceable.

(iv) We express no opinion as to whether a state court outside of the State of New York or a federal court of the United States would give effect to the choice of New York law or jurisdiction provided for in the Warrants.

Our opinion herein is expressed solely with respect to the General Corporation Law of the State of Delaware, and, as to the Warrants constituting valid and legally binding obligations of the Company, the laws of the State of New York. 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 (i) the Shares, when sold and issued in accordance with the Registration Statement and the Prospectus, will be validly issued, fully paid and nonassessable, (ii) the Warrants, when duly executed and delivered against payment therefor as provided in the Registration Statement and the Prospectus, will be valid and legally binding obligations of the Company and (iii) the Warrant Shares, when issued and paid for in accordance with the terms of the Warrants, will be validly issued, fully paid and nonassessable.

COOLEY LLP   101 CALIFORNIA STREET, 5^TH FLOOR, CA   94111-5800
T: (415) 693-2000  F: (415) 693-2222  COOLEY.COM

Geron Corporation
May 26, 2020
Page Three

We consent to the reference to our firm under the caption “Legal Matters” in the Prospectus and to the filing of this opinion as an exhibit to a Current Report on Form 8-K to be filed with the Commission for incorporation by reference into the Registration Statement. This opinion is expressed as of the date hereof, and we disclaim any responsibility to advise you of any changes in the facts stated or assumed herein or any changes in applicable law.

Sincerely,

Cooley LLP

COOLEY LLP   101 CALIFORNIA STREET, 5^TH FLOOR, CA   94111-5800
T: (415) 693-2000  F: (415) 693-2222  COOLEY.COM