The Grammy winners have signed on for a two-week stint in the production, which celebrates jazz icon Duke Ellington's years at Harlem's famous Cotton Club, the Hollywood Reporter said.
The production will officially open at the Brooks Atkinson Theatre on November 13 and Braxton and Babyface will appear from March 18-30 next year.
Other artists set to star in the show include k.D. Lang and Fantasia Barrino.
Braxton and Babyface have also teamed up to record a new duets album - Love, Marriage & Divorce - which is set for release in December.