TONI BRAXTON GOES PUBLIC WITH BIRDMAN

Toni Braxton's finally ready to show off her man onstage, confirming what we already told you -- she and Birdman are banging.

Birdman scored a spot in Toni's show Thursday night at Fox Theatre in Atlanta. Check out the vid ... the Cash Money CEO got a roar from the crowd when she motioned for him to join her and her sisters onstage.

As we reported, the duo's been very close for years, and had some low-key hookups, but this was their true debut. Toni even called him, "boo."

During the show, Toni was presented with the key to the city by councilman Kwanza Hall, and mayor Kasim Reed declared it "Toni Braxton Day." We're told Birdman was front and center for that too. Boo.