Directed by Joe Mantello, the production is to open April 24 at a Shubert theater to be announced.
Midler will play the late Hollywood talent agent Sue Mengers in the one-character play.
This will be the first time Midler will appear on Broadway in more than 30 years. Her last stint was in "Bette! Divine Madness."
"I met Sue Mengers only once, at a dinner party," playwright Logan said in a statement. "The kaftan, constant cigarettes, tinted glasses, and perfect blond hair were much in evidence; so too the deliciously wicked wit and stevedore language.
"But something else fascinated me just as much: a sense of sadness, a deep resignation; a woman whose time had passed her by. At one point, I asked her what had changed most about Hollywood since she had arrived. She didn't hesitate for a second: 'Honey, we used to have fun ... .'
"Later in the evening, she settled back and lit up a joint. There she was: a joint in one hand and a cigarette in the other. At that moment, I knew I had to write the play."
Logan won a Tony Award for his play "Red" and wrote the screenplay for the latest James Bond movie, "Skyfall."