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.

Juvonen Fallon, who runs Flower Films with Drew Barrymore, has been referred to as “the coolest girl in the world” by her husband. Perhaps there’s now another lady in the running?

The couple’s latest addition will join Gary, the pair’s female golden retriever who often appears on his Emmy-nominated talk show.