The novel, which follows detective Hercule Poirot as he attempts to solve who killed an American on a train, was adapted into a 1974 film starring Albert Finney, Lauren Bacall and Ingrid Bergman, who won an Academy Award for her performance.
Christie wrote the plays Witness for the Prosecution, Ten Little Indians and Hidden Horizon. The plays Love from a Stranger and The Fatal Alibi were based on her writing.
Mark Gordon, Simon Kinberg and Ridley Scott are producing the film, which will feature a screenplay by Michael Green.
A five-time Academy Award nominee, Branagh has directed "Cinderella," "Hamlet," "Much Ado About Nothing" and "As You Like It," among others. He made his New York stage debut in 2014 in Macbeth at the Park Avenue Armory.