The movie explores the often-unpredictable bond between the three main characters and how it intersects with their joint passion for professional tennis
Cooper, 41, who has been nominated for four Oscars, including acting and producing 2014's "American Sniper," will make his directorial debut on the movie, while Lady Gaga, 30, will make her feature film lead acting debut.
Warner Bros did not give a release date for the project.
It was remade with Judy Garland and James Mason in 1954 and with Barbra Streisand and Kris Kristofferson in 1976.
In the new film, Grammy-winning Lady Gaga will compose and perform new songs.
The singer made her television acting debut in FX's "American Horror Story: Hotel," playing the vampire Countess, which landed her a Golden Globe best actress in a limited series/TV movie award.