The seven-time Academy Award-winning 1998 motion picture also featured an Oscar-winning screenplay co-written by Stoppard.
The stage production, which is aiming for a London bow, will be produced by Disney Theatrical Prods. in partnership with Sonia Friedman Prods.
Hairspray Tony winner Jack O'Brien will direct the production, which will feature designs by Tony winner Bob Crowley.
No timetable has been announced for the production.
Tom Stoppard is a four-time Tony Award winner for his plays The Coast of Utopia, The Real Thing, Travesties and Rosencrantz and Guildenstern Are Dead. His works for the stage also include Rock 'n' Roll, Arcadia, The Invention of Love, Jumpers, Artist Descending a Staircase and Night and Day. Stoppard won an Academy Award for his screenplay for "Shakespeare in Love."