Jimmy Fallon Welcomes Baby Girl

"I'm the father of a beautiful baby girl. Her name is Winnie Rose Fallon and she's so cute. She's 5 lbs., 9 oz. Me and my wife are so happy," Fallon said during his monologue Wednesday. "Thank you all for all the well-wishes on Facebook and Twitter and the blogs. I'm just so happy."

The Late Night host, 38, and wife Nancy Juvonen Fallon welcomed a baby girl on Tuesday, July 23 at 6:21 a.m., his rep confirms to PEOPLE exclusively.

The first-time parents are "overjoyed about the arrival of their beautiful daughter," the rep tells PEOPLE.

Fallon, who will take over The Tonight Show from Jay Leno next year, and his producer wife, 46, were married in December 2007.