The event will mark the 21st birthday of the charitable organisation, which Sting and his producer-actress wife Trudie Styler founded.
"She's (Gaga) such a great young woman. It's a winning combination -- we're going to have a riotous time up there," contactmusic.com quoted Styler as saying.
"Sting, Elton and Gaga will play together, and the boys will be performing with Dame Shirley, doing a great rendition of Hey Big Spender."
The trio and Dame Shirley will perform together at Carnegie Hall in New York May 13.
