The artists recorded the 1937 Rodgers and Hart show tune as part of Bennett's new album Duets II. The track was previously sung by jazz greats such as Frank Sinatra, Ella Fitzgerald and Sammy Davis Jr.
The video for 'The Lady is a Tramp' features GaGa and Bennett in the minimalistic recording studio with a grand piano as they sing the song.
Bennett recently described GaGa as the most talented artist he has ever met, and has also called the 'You and I' singer "kind, friendly and sweet".
Duets II features collaborations with Michael Bublé and Mariah Carey, as well as the late Amy Winehouse on 'Body and Soul'.
Watch the video for Lady GaGa and Tony Bennett's 'The Lady Is a Tramp' below: