Brad Pitt's Plan B Entertainment will produce the film along with director Murphy.
Mark Ruffalo will play Ned Weeks, the hero of the drama about fear in the early days of the AIDS crisis. Tony winner Joe Mantello played that part in the recent Broadway production.
"The story of a city in denial," The Normal Heart, according to press notes for the Broadway run, "unfolds like a real-life political thriller — as a tight-knit group of friends refuses to let doctors, politicians and the press bury the truth of an unspoken epidemic behind a wall of silence. First produced by Joseph Papp at New York's Public Theater, the play was a critical sensation and a seminal moment in theater history. So ahead of its time was this play that many of the core issues it addresses — including gay marriage, the healthcare system and, of course, AIDS — are just as relevant today as they were when it first premiered."