The Star Wars actor will lead the cast as unhappily married Henry, a playwright who has an affair with another man's wife, although MCGregor's co-stars have yet to be announced.
Previews will begin at the American Airlines Theatre in October, 2014, with Sam Gold as director.
MCGregor is no stranger to the stage - he last performed at London's Donmar Warehouse in 2008 as Iago in a production of Shakespeare's Othello, opposite Chiwetel Ejiofor as the lead character.
Gold's version of The Real Thing will be the play's third run on Broadway - Glenn Close and Jeremy Irons portrayed the leads in a 1984 production, while Jennifer Ehle and Stephen Dillane took over the roles for a revival in 2000. All four stars won Tony Awards for their performances.
Roger Rees and British star Felicity Kendal, who once romanced Stoppard, originated the roles in London in 1982.