O'Hara is a three-time Tony Award nominee who has starred in "South Pacific," "The Pajama Game" and "The Light in the Piazza."
Broderick is a two-time Tony winner whose stage credits include "The Producers," "How to Succeed in Business Without Really Trying" and "Brighton Beach Memoirs."
"Nice Work" -- featuring songs by George and Ira Gershwin with a book by Tony winner Joe DiPietro -- is being directed and choreographed by three-time Tony winner Kathleen Marshall. It is scheduled to open on Broadway in April.
The show "follows Billie Bendix, a tough-as-nails bootlegger who meets up with wealthy playboy Jimmy Winter on the weekend of his nuptials," a synopsis of the show said.
O'Hara and Marshall previously collaborated on "The Pajama Game" and "Bells Are Ringing" at Encores!
"I am over the moon to get to work with the brilliant Kelli O'Hara again. Kelli and Matthew starring together in a romantic screwball comedy and singing Gershwin songs is going to be a total blast," Marshall said in a statement.