Thomas, who was most recently on Broadway in A Naked Girl on the Appian Way, will also be seen this summer in the La Jolla Playhouse's staging of Terrence McNally's Unusual Acts of Devotion.
Race, by the author of American Buffalo, Glengarry Glen Ross, Speed-the-Plow, November and The Cryptogram, will officially open on Broadway Dec. 6.
Mamet will also direct.
The design team will include set designer Santo Loquasto, lighting designer Brian MacDevitt and costume designer Paul Tazewell.
The Barrymore, which was the recent home of the much-in-the-news revival of Mamet's Speed-the-Plow, is located at 243 West 47th Street.