"We were fast friends – friends ever since [our first meeting]," Gaga, 28, told PEOPLE Monday at the taping of their PBS jazz special, Tony Bennett & Lady Gaga: Cheek to Cheek LIVE!, in New York City.
The collaborators initially connected in 2011 when Gaga was performing at the Robin Hood Foundation charity gala and the duo will release their jazz album, Cheek to Cheek, on Sept. 23. Their first single, "Anything Goes," debuted Thursday. Listen below.
"When we were there, I sang a jazz song, 'Orange Colored Sky,' " she says. "Tony heard me sing it, and he asked to meet me after the show. And I said, 'Oh my gosh! Tony Bennett's here!' "
The classically-trained musician and one-time Tisch School of the Arts student says she was "so nervous" to meet the legend.
"I fixed my hair, and my mom was fixing her makeup, and then we went back to meet him," Gaga says. "He said, 'Do you want to do a jazz album together?' And I said, 'Yes, of course I do!' "
"How about that?" Bennett added with a chuckle.
Before recording their own album, Gaga and Bennett – both native New Yorkers – teamed up for "The Lady is a Tramp" on his 2011 album, Duets II.
But what can Little Monsters expect off the new record?
"I listened to the album: I was blown away, and I've known her for how long?" says longtime friend Lady Starlight. "People forget she's first and foremost a musician. She's so legit it's not even funny. It'll be nice to prove to people who don't believe that she can sing or are critical."
All it takes is a gander online to see the "Poker Face" singer and "I Left My Heart in San Francisco" crooner keep in touch outside of the recording studio. Not only did Bennett invite her to lecture with him at the Frank Sinatra School of the Arts, he also drew one of her tattoos!
"I asked Tony to draw me a trumpet, and he sketched me Miles Davis's trumpet. Then I had it tattooed with his last name, Benedetto, underneath," Gaga says. "Just so I would always remember this time together."