The X-Men star will begin rehearsing for his role in the revival of A Life In The Theatre on 23 August (10), according to producer Jeffrey Richards.
A Life In the Theatre, about the relationship between an older performer and a younger actor, was first seen in Chicago, Illinois in 1977 and was later performed off-Broadway.
Neil Pepe, who took charge of the 2008 Broadway revival of Mamet's Speed-the-Plow, will direct. Stewart's younger co-star has yet to be cast.
The veteran star was last seen on Broadway in 2008, playing the title character in Macbeth.