"The baby is here. Isabella arrived yesterday," Damon's brother Kyle told PEOPLE on Monday. Isabella was born Sunday night 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."
This is the first child for the couple. Luciana also has a daughter, Alexia, from a previous marriage.
"He's a terrific uncle and he's going to be a wonderful father," Kyle said of his brother, Matt. "Thankfully, Lucy has some experience, so that will help. Alexia is a terrific girl. They're all really close, they'll be an intimate family."
As for getting parenting tips from his best friend – and fellow new dad – Ben Affleck, Damon told PEOPLE last month, "I'm sure I'll be asking him for plenty of diaper advice."
Damon and Luciana, who met in Miami Beach in 2003 while he was filming Stuck on You, married in December in a surprise ceremony at Manhattan's City Hall.
"They were thrilled," said New York City Mayor Michael Bloomberg, who was one of the few to attend the private nuptials.
It was the first marriage for Damon, 35, and the second for Luciana, 30.
"I like Lucy a lot. They make a fantastic couple," Damon's brother Kyle told PEOPLE at the time.
Next up for Damon: He'll reprise his role as Linus Caldwell in Ocean's 13. Production is scheduled to start in July for a summer 2007 release.