Supplemental Prospectus (Form 424B3)

Filed Pursuant to Rule 424(b)(3)

Registration No. 333-284263

PROSPECTUS SUPPLEMENT

To Prospectus dated February 7, 2025

Up to 73,333 Shares of Common Stock

Up to 31,145,319 Shares of Common Stock Issuable Upon Conversion of Notes

Up to 600,000 Shares of Common Stock Issuable Upon Exercise of Warrants

Adagio Medical Holdings, Inc.

This prospectus supplement updates and supplements the information contained in the prospectus dated February 7, 2025 (as may be supplemented or amended from time to time, the "Prospectus"), which forms part of our registration statement on Form S-1 (File No. 333-284263) with the information contained in our Current Report on Form 8-K that was filed with the Securities and Exchange Commission on October 24, 2025 (the "Current Report"). Accordingly, we have attached the Current Report to this prospectus supplement.

The Prospectus and this prospectus supplement relate to the offer, sale or other disposition from time to time of up to 31,818,652 shares of our common stock, $0.0001 par value per share (the "Common Stock"), by the selling stockholders named in this prospectus or their permitted transferees (the "selling stockholders"), consisting of (i) 73,333 shares of Common Stock (the "Registration Delay Shares") issued pursuant to the terms of the Convert Waivers (as defined below), (ii) up to 31,145,319 shares of Common Stock (excluding the shares of Common Stock underlying the Warrants (as defined below)) (the "Convertible Note Shares") issuable upon the conversion of those certain 13% senior secured convertible notes, with a conversion price of $10.00 per share, subject to adjustment (the "Convertible Notes") issuable pursuant to that certain securities purchase agreement, dated February 13, 2024, by and among us and those certain investors (the "Convert Investors"), and any assignment thereunder (the "Convertible Security Subscription Agreement"), and that certain note purchase agreement, dated February 13, 2024, by and among us, Adagio Medical, Inc., a Delaware corporation, and that certain investor party thereto, and (iii) up to 600,000 shares of Common Stock (the "Warrant Shares") issuable upon exercise of those warrants to purchase shares of Common Stock, with an exercise price of $24.00 per share (the "Warrants"), issued pursuant to the Convertible Security Subscription Agreement.

You should read this prospectus supplement in conjunction with the Prospectus. This prospectus supplement is qualified by reference to the Prospectus except to the extent that the information in this prospectus supplement supersedes the information contained in the Prospectus. This prospectus supplement is not complete without, and may not be delivered or utilized except in connection with, the Prospectus. If there is any inconsistency between the information in the Prospectus and this prospectus supplement, you should rely on the information in this prospectus supplement. Terms used in this prospectus supplement but not defined herein shall have the meanings given to such terms in the Prospectus.

Our Common Stock is listed on The Nasdaq Capital Market under the symbol "ADGM". On October 23, 2025, the last reported sales price of our Common Stock was $1.31 per share.

We are an "emerging growth company" as defined under U.S. federal securities laws and, as such, have elected to comply with reduced public company reporting requirements. This prospectus complies with the requirements that apply to an issuer that is an emerging growth company.

Investing in our securities involves a high degree of risk. You should review carefully the risks and uncertainties described in the section titled "Risk Factors" beginning on page 10 of the prospectus, and under similar headings in any amendments or supplements to the prospectus.

Neither the Securities and Exchange Commission nor any state securities commission has approved or disapproved of these securities, or passed upon the accuracy or adequacy of the prospectus. Any representation to the contrary is a criminal offense.

The date of this prospectus supplement is October 24, 2025.

UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 8-K

CURRENT REPORT

Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934

Date of Report (Date of earliest event reported): October 23, 2025

ADAGIO MEDICAL HOLDINGS, INC.

(Exact name of registrant as specified in its charter)

Delaware	001-42199	99-1151466
(State or other jurisdiction of incorporation)	(Commission File Number)	(I.R.S. Employer Identification No.)

26051 Merit Circle, Suite 102 Laguna Hills, CA		92653
(Address of principal executive offices)		(Zip Code)

(949) 348-1188

(Registrant's telephone number, including area code)

Not Applicable

(Former name or former address, if changed since last report)

Check the appropriate box below if the Form 8-K filing is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions:

¨	Written communications pursuant to Rule 425 under the Securities Act (17 CFR 230.425)

¨	Soliciting material pursuant to Rule 14a-12 under the Exchange Act (17 CFR 240.14a-12)
¨	Pre-commencement communications pursuant to Rule 14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))

¨	Pre-commencement communications pursuant to Rule 13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c))

Securities registered pursuant to Section 12(b) of the Act:

Title of each class	Trading Symbol(s)	Name of each exchange on which registered
Common Stock, par value $0.0001 per share	ADGM	The Nasdaq Stock Market LLC

Indicate by check mark whether the registrant is an emerging growth company as defined in Rule 405 of the Securities Act of 1933 or Rule 12b-2 of the Securities Exchange Act of 1934.

Emerging growth company x

If an emerging growth company, indicate by check mark if the registrant has elected not to use the extended transition period for complying with any new or revised financial accounting standards provided pursuant to Section 13(a) of the Exchange Act. ☐

Item 5.08 Shareholder Director Nominations

On October 23, 2025, the Board of Directors of Adagio Medical Holdings, Inc. (the "Company") established December 15, 2025 as the date of the Company's 2025 Annual Meeting of Stockholders (the "2025 Annual Meeting"). The time and location of the 2025 Annual Meeting will be set forth in the Company's definitive proxy statement for the 2025 Annual Meeting to be filed with the Securities and Exchange Commission (the "SEC"). The record date for determining stockholders entitled to notice of, and to vote at, the 2025 Annual Meeting will be the close of business on October 31, 2025.

Because the Company did not hold a 2024 Annual Meeting of Stockholders, the Company is filing this Current Report on Form 8-K to inform stockholders of the date of the 2025 Annual Meeting and to provide the due date for the submission of any qualified stockholder proposals or qualified stockholder director nominations.

Stockholders who intend to present proposals for inclusion in the Company's proxy materials for the 2025 Annual Meeting pursuant to Rule 14a-8 ("Rule 14a-8") promulgated under the Securities and Exchange Act of 1934, as amended (the "Exchange Act"), must ensure that such proposals are delivered to or mailed and received by the Company's Secretary at Adagio Medical Holdings, Inc., 26051 Merit Circle, Suite 102 Laguna Hills, CA, no later than November 3, 2025, which the Company has determined to be a reasonable time before it expects to begin to deliver and make available its proxy materials for the 2025 Annual Meeting, and must furthermore comply with all applicable requirements of Rule 14a-8.

Pursuant to the Company's amended and restated bylaws ("Bylaws"), for stockholder director nominations or other proposals to be considered at an annual meeting, the stockholder must give timely notice thereof in writing to the Company's Secretary at Adagio Medical Holdings, Inc., 26051 Merit Circle, Suite 102 Laguna Hills, CA, no later than November 3, 2025. To be timely for the 2025 Annual Meeting, a stockholder's notice must be delivered to or mailed and received by the Company's Secretary at the Company's principal executive offices not later than November 3, 2025, the tenth calendar day following the date of this Current Report on Form 8-K publicly announcing the date of the 2025 Annual Meeting. A stockholder's notice to the Secretary must also set forth the information required by the Bylaws.

In addition to satisfying the foregoing requirements under the Bylaws, to comply with the SEC's universal proxy rules, stockholders who intend to solicit proxies in support of director nominees other than the Company's nominees must provide notice to the Company that sets forth the information required by Rule 14a-19 under the Exchange Act no later than November 3, 2025.

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.

Dated: October 24, 2025

	Adagio Medical Holdings, Inc.
	By:	/s/ Deborah Kaster
	Name:	Deborah Kaster
	Title:	Chief Financial Officer