Streep will play opera legend Maria Callas in the screen version of the McNally drama, which debuted on Broadway in 1995.
Mike Nichols, who previously worked with Hollywood favorite Streep on "Silkwood," "Angels in America" and "Heartburn," will direct. Filming is scheduled to begin in January 2015.
No official announcement has been made about the "Master Class" film. Oscar winner Faye Dunaway had long been attached to a screen version of the work, which concerns Callas' legendary classes at Juilliard in 1971.
Master Class opened at Broadway's John Golden Theatre on Nov. 5, 1995, starring Zoe Caldwell as the famed opera diva and Karen Kay Cody, Audra McDonald and Jay Hunter Morris as three of her master class attendees. Caldwell and McDonald both won Tonys for their performances; Caldwell was succeeded in the demanding role by Patti LuPone — who also took the play to London — and Dixie Carter. Dunaway headed the tour of the play, and she received Chicago's Sarah Siddons Society Award for her performance.