A Raisin in the Sun director Kenny Leon is helming the show for Roundabout Theatre Company.
The limited engagement at the American Airlines Theatre will begin preview performances on Dec. 27. The production is scheduled to open officially on Jan. 21.
Grier recently starred in Porgy and Bess and Underwood headlined A Streetcar Named Desire.
A Soldier's Play follows a black investigator trying to solve the murder of a black sergeant on a Louisiana Army base in 1944.
"Coming back to BROADWAY! #ASoldiersPlay. The holidays-March 15th? Hope to see ya. First time ON-Broadway. Original Off-Broadway cast in 1982 included Denzel Washington, Samuel L Jackson, Jim Pickens, Brent Jennings, David Alan Grier. #NEC @roundaboutnyc #MainStage #pulitzerprize," Underwood tweeted.
"We comin, y'all beta git ready! #SoldiersPlay," Grier wrote in his own post.