The evening will be themed around the theater's current revival of Our Town.
The off-Broadway institution has announced three of the titles in its upcoming 2014-2015 season.
The honor will be bestowed during the 2014 Tony Awards on June 8.
Jason Gotay, Remy Zaken, and Randy Jones will lead the cast of the political piece.
Gyllenhaal withdrew from the off-Broadway production in February because of scheduling conflicts.
The two-time Tony winner leads the cast of Sarah Treem's world premiere drama.
Cast members Jefferson Mays, Bryce Pinkham, Lisa O'Hare, and Lauren Worsham will perform.
Tony nominee Kenny Leon directs the rap-inspired production, beginning performances in May.
The event will honor Hairspray and Smash composer/lyricist Marc Shaiman and director/writer Scott Wittman.
The cast also includes Robin De Jesús, Todd Buonopane, and Mykal Kilgore.