Rose Byrne has welcomed her first child with partner Bobby Cannavale.

The Australian actress gave birth to a boy, Rocco, on February 1, the proud father revealed on CBS' The Late Show with Stephen Colbert.

"You know, I didn't do anything ... and I'm so tired," the Vinyl star, 45, told Colbert.

"I think I've gained 28 pounds [12.7 kg] since Monday."

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The 36-year-old Byrne debuted her growing baby bump at LAX airport back in October, but the notoriously private couple have revealed few details of the pregnancy.

Byrne and Cannavale began dating in 2012 and co-starred in films Adult Beginners, Annie and Spy.

Cannavale already has a 10-year-old son, Jake, from his marriage to screenwriter Jenny Lumet, which ended in 2003.

- AAP