Bridesmaids star Byrne has welcomed a son with her partner, fellow actor Bobby Cannavale.
Bobby told Stephen Colbert Rose, 36, gave birth last Monday.
"I had a baby on Monday, yes," he said on The Late Show.
"You know, I didn't do anything. We [fathers] don't do anything and I'm so tired. I think I've gained 28 pounds since Monday."
The baby boy's name is Rocco, he confirmed.
Bobby, 45, said legendary star Al Pacino gave the couple a cake made out of diapers.
Rocco is Rose's first son, while Bobby has a 20-year-old son from a former marriage.
The couple have been together for three years, even attending the Logies in Australia last year.
Rose began her career alongside Heath Ledger in Australian hit, Two Hands. She has since risen to megastardom in box office hits like Bridesmaids and the X-Men franchise. Her latest film X-Men: Apocalypse is due to hit cinemas in May.
Bobby is known for his roles in Blue Jasmine, alongside Cate Blanchett, and Boardwalk Empire. He is currently starring in a new HBO series Vinyl, to premiere on Foxtel on February 15.