Paltrow will play Catherine in David Auburn's play, which previews from May 9, opens on May 15 and runs until June 15.
John Madden, who directed Paltrow in "Shakespeare in Love," is to direct the Donmar production. Proof has won multiple awards including the Pulitzer Prize for Drama and the Tony Award for Best Play.
Paltrow is a favorite with British film audiences and is likely to prove a hit with theatregoers as well. The Proof will be in the performance.
Reports in Variety have Paltow likely to star in the film version of Proof should her stage appearance go well.