UNITED STATES

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

PURSUANT TO RULE 13a-16 OR 15d-16

OF THE SECURITIES EXCHANGE ACT OF 1934

For the month of October 2025

Commission File Number 001-42254

Rezolve AI plc

(Translation of registrant’s name into English)

21 Sackville Street,

London, W1S 3DN

United Kingdom

(Address of principal executive offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Form 20-F  ☒ Form 40-F  ☐

EXPLANATORY NOTE

On October 22, 2025, Rezolve AI plc (the "Company") announced the appointment of Arthur Yao as Chief Operating and Financial Officer of the Company and the appointment of Richard Burchill as the Group Finance Director of the Company. A copy of the press release is furnished as Exhibit 99.1 to this Report on Form 6-K and is incorporated herein by reference.

The information included in this Report on Form 6-K (including Exhibit 99.1) is hereby incorporated by reference into the Company’s Registration Statements on Forms F-3 (File No. 333-290523 and File No. 333-290639) (including any prospectuses forming a part of such registration statements) and to be a part thereof from the date on which this Report on Form 6-K is filed, to the extent not superseded by documents or reports subsequently filed or furnished.

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 22, 2025