The young star and LaBeouf will play orphaned brothers who kidnap a wealthy man, played by Baldwin, only for the siblings to form an odd bond with their victim.
Commenting on the casting news on Twitter.com, the 30 Rock funnyman writes, "It's Tom Sturridge, Shia LaBoeuf and moi. Gonna be interesting."
The Lyle Kessler drama, which was adapted into a 1987 film starring Albert Finney and Matthew Modine, will begin previews at the Gerald Schoenfeld Theatre in New York on 19 March (13), and will officially open on 7 April (13).
Sienna Miller's rumoured fiance will join LaBeouf as a Broadway newbie, but it won't be Sturridge's first time on stage - the On the Road actor has previously honed his theatre skills in London in 2009 play Punk Rock, for which he won the U.K. Critics' Circle Theatre Award for Best Newcomer.