Adapted and directed by Sean Foley, the new play is based on the Ealing comedy classic that originally premiered in 1951 starring Alec Guinness and Joan Greenwood.
The new production sees Mangan star as Sidney Stratton, a man who develops a fabric that never gets dirty and never wears out, earning the ire of manufacturers and trade unions in the process.
Mangan was last seen on stage in Ian Rickson's production of The Birthday Party, while Tointon recently starred as Olivia in the RSC's Twelfth Night. The world premiere will feature 14 actor-musicians and design by Michael Taylor, with members of the creative team and cast to be announced.
The Man in the White Suit will run at Theatre Royal Bath from 5 to 21 September, before transferring to Wyndham's Theatre where it begins previews on 26 September with an opening night on 8 October.