Matt Damon Has Baby Girl

The baby girl, named Isabella, was born on Sunday in Miami.  "Mother and Isabella are doing fine," Damon’s rep Jennifer Allen, confirmed to PEOPLE. "The family is very happy and everyone’s healthy."

Luciana has a daughter, Alexia, from a previous marriage.  Damon, 35, and his 30 year-old wife met in 2003 when he was filming the movie Stuck on You.  They were married in December, 2005.