Brinkley's run in the Broadway version of the musical comes to an end on June 19. The 57-year-old will reportedly join the London production this summer.
Showbiz 411 reports that Brinkley and co-star Amra-Faye Wright will appear for a limited engagement from July.
Brinkley recently revealed that her ex-husband Billy Joel gave her tips to succeed on Broadway.
The actress will present an award at this year's Tony Awards.
> Christie Brinkley: "I haven't given up on love"