The pair, who are engaged, will star in the show, which will run from October this year.
Cy Coleman's musical, which premiered on Broadway in 1989, weaves together the tale of a writer trying to get his novel turned into a screenplay and the fictional story of the movie itself. The 1993 London production starred Roger Allam, Haydn Gwynne and Henry Goodman.
Hadley Fraser will be returning to the Donmar following his performance in Rourke's production of Coriolanus earlier this year. His other stage credits include The Pajama Game (Chichester Festival Theatre), The Machine (Manchester International Festival) and Les Miserables (West End).
Rosalie Craig's theatre credits include The Light Princess, Table, London Road (National), Ragtime (Open Air) and Finding Neverland (Leicester). She is about to appear in Chichester Festival Theatre's Miss Julie.