The former "Frasier" and "Cheers" star will share the stage with Douglas Hodge in the acclaimed Menier Chocolate Factory production, which was previously a huge hit in London.
The show is to begin previews April 6 and open April 18 at New York's Longacre Theatre.
The reconceived production is choreographed by Lynne Page and directed by Terry Johnson.
Rehearsals are to begin March 1.
"I had a wonderful experience playing Henry Higgins in the New York Philharmonic's 'My Fair Lady' in 2007, which made me long to perform in a musical on Broadway," Grammer said in a statement. "Jerry Herman and Harvey Fierstein's wonderfully funny and touching show is about being true to yourself and the challenges you face as a parent, as a spouse and as a family. I cannot wait to work with Douglas Hodge and to sing these magnificent songs every night."
Grammer will play Georges, the owner/emcee of the St. Tropez nightclub where his partner, Albin, stars as the drag queen headliner, Zaza. Hodge will play Albin.
Grammer has previously appeared on Broadway in the dramas "Macbeth" and "Othello."