Sean Mathias is to direct the productions, which will be performed in a rotating schedule this fall.
The theater and performance dates, as well as additional casting and other members of the creative team, will be announced shortly, producers said.
The British actors are renowned stage veterans who have also enjoyed successful screen careers. The pair have played foes Magneto and Professor Xavier in three "X-Men" blockbusters to date.
McKellen also has starred in "The Lord of the Rings" trilogy and "The Hobbit: An Unexpected Journey," while Stewart led the cast of the "Star Trek: The Next Generation" movies and TV series.
McKellen and Stewart co-starred in 2009 in London in Samuel Beckett's "Waiting for Godot" -- which features two men passing the time waiting for someone who may or may not arrive. Harold Pinter's "No Man's Land" centers on a failed poet staying as a guest in the home of an upper-class man he met in a pub.