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 December 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

Closing of the CrownPeak Acquisition

As previously disclosed, on December 1, 2025, Rezolve AI plc (the “Company”) entered into a sale and purchase agreement with CrownPeak Technology Holdings, Inc, a Delaware corporation, pursuant to which the Company agreed to the acquisition of the issued share capital of CrownPeak Intermediate Holdings, Inc., a Delaware corporation (the “CrownPeak Acquisition”).

The CrownPeak Acquisition closed on December 5, 2025, following the satisfaction of the closing conditions.

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: December 5, 2025