Gaga, 28, got engaged to the "Chicago Fire" star last month after dating for four years.
"They invited me to do it and, of course, I will," said Bennett, who teamed up with Gaga on the album "Cheek to Cheek".
The 88-year-old singer called Kinney a wonderful man, reported the New York Post.
"I love it. She's marrying a very wonderful man, very talented and very handsome. I think he's going be highly successful in films. He's a very nice person," he said.