Matt Damon, Wife Have a Girl

Matt Damon and his wife, Luciana Bozan, have welcomed a baby girl named Isabella, PEOPLE has learned exclusively.

"The baby is here. Isabella arrived yesterday," Damon's brother Kyle told PEOPLE on Monday. The baby weighed in at 7 lbs., 7 oz.

"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. Bozan 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."

Late last year, Damon said at a press conference that he "longed for" fatherhood. "But I've got to learn how to be a good disciplinarian," he said, "'cause I'm a professional uncle right now."

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 Bozan, 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 Bozan, 30, a bartender turned interior designer.

"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.

Source: PEOPLE