Exhibit 10.4

BOARD RIGHTS AGREEMENT

This Board Rights Agreement (this “Agreement”) is entered into as of September 23, 2026 (the “Effective Date”), by and between Celularity Inc., a Delaware corporation (the “Company”), and the Philip & Daniele Barach Family Trust, a trust formed under the laws of California (the “Trust”; the Company and the Trust are referred to herein individually as a “Party” and collectively as the “Parties”).

WITNESSETH:

WHEREAS, the Company, the Trust and the other investors party thereto (collectively, the “Other Investors”; the Trust and the Other Investors, collectively, the “Investors”) are parties to that certain Securities Purchase Agreement dated as of September 23, 2026, by and among the Company, the Trust and the Other Investors (as amended, supplemented or otherwise modified, the “Purchase Agreement”; capitalized terms not otherwise defined herein shall have the respective meanings set forth in the Purchase Agreement), pursuant to which the Company may issue and sell senior secured convertible promissory Notes in an aggregate principal amount of up to $25,000,000, together with related Warrants; and

WHEREAS, in connection with the purchase of the Notes by the Investors and as a material inducement to such purchase, the Company has agreed that its Board will consist of five (5) directors comprised of persons designated pursuant to the terms hereof, and that the Company will prepare and file with the Securities and Exchange Commission a Schedule 14f-1 information statement (the “Schedule 14f-1 Information Statement”) and take the other actions required to effectuate such change in Board composition, in each case on the terms and subject to the conditions set forth in this Agreement.

NOW, THEREFORE, in consideration of the mutual covenants and agreements contained herein, and other good and valuable consideration, the receipt and sufficiency of which are acknowledged, the Parties agree as follows:

1. Board Composition; Trust Directors

Effective upon the first issuance of Notes under the Purchase Agreement, and thereafter until the termination of this Agreement, the Company’s board of directors (the “Board”) shall consist of five (5) directors, comprised of: (i) Bob Hariri and Peter Diamandis (collectively, the “Incumbent Directors”); (ii) two (2) directors designated by the Trust (the “Trust Directors”); and (iii) one (1) director nominated by the Incumbent Directors and reasonably acceptable to the Trust Directors (the “Independent Director”). The initial Trust Director shall be Philip Barach, and the second Trust Director and the initial Independent Director shall be identified and appointed in accordance with Section 2. The Company shall take all necessary corporate action, subject to applicable law, Nasdaq rules and the Company’s certificate of incorporation and by-laws, to cause the Board to conform to the composition required by this Section 1.

2. Appointment; Nomination; Board Action

The Company shall take all necessary corporate action, subject to applicable law, Nasdaq rules and the Company’s certificate of incorporation and by-laws, to cause (i) the Trust Directors to be appointed to the Board as soon as practicable following the first issuance of Notes and in compliance with Rule 14f-1 under the Exchange Act and (ii) the Independent Director, nominated by the Incumbent Directors and reasonably acceptable to the Trust Directors, to be named and appointed to the Board as soon as practicable following the first issuance of Notes and in compliance with Rule 14f-1 under the Exchange Act, in each case no earlier than ten (10) days after the mailing of the Schedule 14f-1 Information Statement to stockholders and, with respect to the Independent Director, in no event later than thirty (30) days after the first issuance of Notes. For the avoidance of doubt, the appointment of the Trust Directors and the Independent Director shall not be a condition precedent to the closing of the purchase and sale of the Notes under the Purchase Agreement. Such actions may include increasing or decreasing the size of the Board, accepting resignations, filling vacancies and appointing the applicable designee or nominee to the Board.

As soon as reasonably practicable after the date hereof, the Trust shall designate the second Trust Director, and the Company shall use its best efforts to present the identity of the proposed Independent Director to the Trust Directors then in office (or, if there are such Trust Directors in office yet, to the Trust) for approval.

Following the appointment of the Trust Directors and the Independent Director, the Company shall include each of the Trust Directors and the Independent Director in the Company’s slate of nominees for election to the Board at each applicable annual or special meeting of stockholders at which the applicable class of directors is up for election. The Company shall recommend that stockholders vote in favor of the election of each such nominee, solicit proxies in favor of their election in the same manner and to the same extent as the Company solicits proxies in favor of the Company’s other nominees, and otherwise support the election of each such nominee in a manner no less favorable than the Company supports its other nominees.

The Company shall not take any action to remove any Trust Director from the Board without Cause unless requested in writing by the Trust. The Company shall not take any action to remove the Independent Director from the Board without Cause unless requested in writing by the Incumbent Directors. “Cause” means (i) a final, non-appealable conviction of, or plea of guilty or nolo contendere to, a felony or crime involving fraud, dishonesty or moral turpitude, willful misconduct that is materially injurious to the Company, or (ii) a determination by the directors of the Company other than the applicable Trust Director or Independent Director (the “Disinterested Directors”), supported by an opinion of outside counsel, that such director is prohibited from serving as a director under applicable law or Nasdaq rules.

3. Schedule 14f-1 Filing

The Company shall prepare and file with the Securities and Exchange Commission, promptly following (or concurrently with) the first issuance of Notes, a Schedule 14f-1 Information Statement in compliance with Rule 14f-1 under the Exchange Act and Section 14(f) of the Exchange Act.

The Company shall mail or otherwise furnish the Schedule 14f-1 Information Statement to the Company’s stockholders of record promptly following its filing with the Securities and Exchange Commission.

The Company shall use commercially reasonable efforts to take all actions necessary to effectuate the change in the composition of the Board as promptly as practicable and in compliance with Rule 14f-1 under the Exchange Act.

4. Interim Covenants

Until the Board contains all five (5) directors in the composition required by Section 1, including the Incumbent Directors, the Trust Directors and the Independent Director, the Company covenants that:

(i) The Company shall not use the proceeds from the issuance of the Notes for anything except: (a) payroll; (b) payments in the ordinary course to creditors not to exceed $100,000 to any one creditor; (c) specific payments listed on Schedule A attached to this Agreement; or (d) payments approved in advance in writing by the Trust; and

(ii) The Company shall not enter into any contract or agreement that would involve the potential expenditure of more than $100,000 without the prior written consent of the Trust.

The restrictions set forth in this Section 4 shall automatically terminate upon the appointment of all directors in compliance with the required Board composition set forth in Section 1.

5. Observer Rights.

For so long as this Agreement remains in effect, if and to the extent that any Trust Director is not a duly appointed or elected director of the Company, the Trust shall be entitled to designate at any time and from time to time one (1) non-voting observer reasonably acceptable to the Company (an “Observer”) to attend each and any meeting of the Board and any committee and subcommittee of the Board. The Company shall give to the Observer copies of all notices, minutes, consents and other materials and information given to the directors of the Company in connection with any such meeting at the same time that such notices, minutes, consents or other materials or information are given to such directors. A majority of the Board or committee or subcommittee, as applicable, shall have the right to exclude the Observer from portions of meetings of the Board or committee or subcommittee or omit to provide the Observer with certain information if such members of the Board in its good faith discretion, including without limitation, based on the advice of Company counsel, that such exclusion or omission may be necessary in order to (a) preserve the Company’s attorney-client privilege, (b) fulfill the Company’s obligations with respect to confidential or proprietary information of third parties or (c) to avoid a potential breach of the fiduciary obligations of the Board to the Company and/or its stockholders.

6. Reimbursement; Expenses; Compensation

Each Trust Director and the Independent Director shall be entitled to the same non-employee director compensation, including cash retainers, equity compensation and expense reimbursement, if any, as is provided to similarly situated non-employee directors of the Company pursuant to the Company’s non-employee director compensation policy as in effect from time to time, unless otherwise agreed in writing by the Company and the applicable Trust Director or Independent Director.

7. Replacement; Vacancies; Qualifications

The Company shall be required to remove or replace any Trust Director at any time upon written notice by the Trust to the Company. In the event that any Trust Director ceases to serve as a director for any reason, including death, disability, resignation, removal, disqualification or failure to be elected, the applicable designating party shall have the right to designate a replacement Trust Director, and the Company shall take all necessary corporate action, subject to applicable law, Nasdaq rules and the Company’s certificate of incorporation and by-laws, to cause such replacement Trust Director to be appointed to the Board as promptly as practicable. In the event that the Independent Director ceases to serve as a director for any reason, the Incumbent Directors shall have the right to nominate a replacement Independent Director reasonably acceptable to the Trust Directors, and the Company shall take all necessary corporate action, subject to applicable law, Nasdaq rules and the Company’s certificate of incorporation and by-laws, to cause such replacement Independent Director to be appointed to the Board as promptly as practicable. Any replacement Trust Director shall be subject to the same qualification and approval standards set forth in Section 1, and any replacement Independent Director shall be subject to the same nomination and approval standards set forth in Section 1. If the Company does not approve a proposed replacement Trust Director in accordance with Section 1, the applicable designating party shall have the right to propose an alternative replacement Trust Director, and if the Trust Directors do not approve a proposed replacement Independent Director, the Incumbent Directors shall have the right to propose an alternative replacement Independent Director.

8. Term

This Agreement shall commence on the Effective Date and continue until the earliest to occur of: (a) the date on which no Notes remain outstanding or (b) the consummation of a Change of Control of the Company.

9. No Prohibition on Investor Activities

Nothing in this Agreement shall (a) limit any Investor’s or its affiliates’ ability to acquire, hold, vote, or dispose of securities of the Company, subject to applicable law; (b) prohibit any Investor from engaging in ordinary-course investment activities or engaging in communications with the Company’s officers and directors; or (c) require any Investor to vote or act in any particular manner with respect to the Company’s securities. Nothing in this Agreement shall restrict the rights of any Investor and its affiliates under the Purchase Agreement, the Notes, the Warrants or any other Transaction Document.

10. Remedies; Equitable Relief

The Parties acknowledge that a breach of Sections 2, 3, 4, 5 or 7 may cause irreparable harm to the Trust for which monetary damages would be an inadequate remedy. Accordingly, the Trust shall be entitled to seek equitable relief, including injunction and specific performance, in addition to any other remedies available at law or in equity, without the necessity of posting bond or the proof of actual damages.

11. Miscellaneous

(a) Entire Agreement. This Agreement constitutes the entire understanding of the Parties with respect to the subject matter hereof and supersedes all prior and contemporaneous understandings, agreements, and representations, whether written or oral.

(b) Amendments; Waivers. No amendment, modification, or waiver of any provision of this Agreement shall be effective unless in writing and signed by the Company, with approval by a majority of the Disinterested Directors or a special committee of Disinterested Directors, and the Trust.

(c) Assignment. This Agreement and the rights and obligations hereunder may not be assigned by the Trust without the prior written consent of the Company and any purported or attempted assignment without such consent shall be void and of no force and effect; provided that the Trust may assign its rights hereunder to any permitted transferee of Notes, Conversion Shares, Warrants or Warrant Shares in accordance with the Purchase Agreement and the other Transaction Documents if such transferee agrees in writing to be bound by this Agreement. The Company may not assign this Agreement without the Trust’s prior written consent.

(d) Notices. All notices shall be in writing and delivered by hand, by nationally recognized overnight courier, or by email (with confirmation of transmission), to the addresses as a Party may designate in writing. Notices shall be deemed given when received.

(e) Governing Law; Jurisdiction; Jury Waiver. This Agreement shall be governed by and construed under the laws of the State of Delaware, without regard to conflicts of law principles. Each Party irrevocably submits to the exclusive jurisdiction of the state and federal courts located in New Castle County, Delaware for any dispute arising out of or relating to this Agreement and waives any objection to venue or forum. EACH PARTY HEREBY WAIVES ANY RIGHT TO A TRIAL BY JURY TO THE FULLEST EXTENT PERMITTED BY LAW.

(f) Severability. If any term of this Agreement is held invalid or unenforceable, such term shall be enforced to the maximum extent permissible and the remaining terms shall remain in full force and effect.

(g) Counterparts; Electronic Signatures. This Agreement may be executed in counterparts, each of which shall be deemed an original and all of which together constitute one instrument. Signatures delivered by electronic transmission shall be deemed original signatures.

(h) No Third-Party Beneficiaries. This Agreement is solely for the benefit of the Parties and their permitted assigns and does not confer any rights upon any other person or entity.

(i) Interpretation. The headings are for convenience only and shall not affect interpretation. “Including” means “including without limitation.”

(j) Costs and Fees. Each Party shall bear its own costs and expenses in connection with the negotiation and execution of this Agreement.

(k) Independent Status. Nothing herein shall be construed to create a partnership, joint venture, or agency relationship between the Parties.

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IN WITNESS WHEREOF, the Parties have executed this Board Rights Agreement as of the Effective Date.

SCHEDULE A

Specific Payments

The following specific payments are approved for purposes of Section 4(i)(c):