Kathleen Marshall is choreographing and directing the show, which features music and lyrics by Cole Porter. The original book was penned by P.G. Wodehouse, Guy Bolton, Howard Lindsay and Russel Crouse. The musical's new book was written by Timothy Crouse and John Weidman.
Previews are slated to begin March 10, with an official opening night set for April 7 at the Stephen Sondheim Theatre in Manhattan.
Grey, a Tony and Academy Award winner, has previously starred in Broadway's "Cabaret," "George M!," "Goodtime Charlie," "The Grand Tour" and "Wicked."
Foster's Broadway credits include "The Drowsy Chaperone" and "Shrek The Musical."