The Born This Way star and the 86-year-old Blue Velvet singer previously performed a duet for one of Tony's albums, and they were rumoured to be planning to make a jazz record together.
Gaga has now revealed the collaboration is definitely in the pipeline by tweeting a picture of the pair, with the message: "And here's me and my handsome date, I simply cannot wait for our album together, he's my darling."
Last year Tony told Rolling Stone that he would be working with Gaga.
The singer, who said he refers to 26-year-old Gaga as "the musical Picasso", said: "I'm looking forward to it because a lot of people don't know it, but she's a phenomenal jazz singer."
Lady Gaga is due to release her fourth album ARTPOP this year, but her producer friend Zedd recently revealed she still has a lot of work to do on the record.