The proud dad confirmed the news during a guest appearance on The Late Show with Stephen Colbert on Friday.
“I had a baby on Monday, yes,” the 45-year-old said.
While both he and Rose have stayed mum on a lot of the details surrounding their child, Bobby did reveal that they’d named their son Rocco and both mum and baby are doing well.
“You know, I didn’t do anything. We (men) don’t do anything and I’m so tired. I think I’ve gained 28 pounds (12kg) since Monday.”
“I mean, I’m not kidding you. Like, this jacket fit so well, like, last Thursday. But I’ve been eating so much.”
This is the first child for 36-year-old Rose, who debut her growing baby bump back in October. Bobby already has a 10-year-old son, Jake, from his marriage to screenwriter Jenny Lumet, which ended in 2003.
Rose and Bobby started dating back in 2012. Since then, they’ve co-stared together on projects including Annie, Adult Beginners and Spy.
While the duo are notoriously private about their personal life, Bobby called his leading lady the “love of my life” when accepting his award for Outstanding Supporting Actor in a Drama Series at the 2013 Emmys.
Congratulations to the happy couple!