Oscar-winning screenwriter Aaron Sorkin, who adapted the movie from Molly Bloom's memoir of the same name, will make his directorial debut with the film, reported the Entertainment Weekly.
Chastain, 39, will play the lead role of Bloom, who ran an exclusive poker game attended by Hollywood stars, athletes, business tycoons, and Russian mobsters for years before she was arrested by the FBI.
Elba, 43, will portray her criminal defense lawyer.
"The casting of Jessica and Idris in the two lead roles is any filmmaker's dream come true. They're two of the greatest actors of their generation, paired for the first time, and their chemistry will be electric," Sorkin said while announcing the news.