Directed by Daniel Sullivan, the drama is to begin performances March 19 and to open April 7 at Schoenfeld Theatre.
This will mark the first Broadway staging of the play, as well as LaBeouf's debut on the Great White Way.
"In the play, two orphaned brothers are living in a decrepit North Philadelphia row house. Treat, the eldest, played by LaBeouf, supports his damaged younger sibling by petty thievery, and makes the house a virtual prison for the seemingly simple-minded Phillip," a synopsis said. "One night he kidnaps a rich older man, Harold [played by Baldwin,] who turns out to have his own motives and becomes the father figure the boys have always yearned for."
Casting for the role of Phillip will be announced soon, producers said.