Matt Damon's wife has given birth to a baby girl named Isabella, the couple's first child together, a spokesperson for the actor of movies such as The Bourne Supremacy said on Monday.

"Mother and baby - everyone - is wonderful, fine," publicist Jennifer Allen said. The baby was born Sunday in a Miami hospital, Allen said. No other details were released.

Damon, 35, and wife Luciana, 30, married in December in New York City. She has a seven-year-old daughter from a previous marriage. It was the first marriage for Damon, 35.

The actor rose to stardom in 1997 low-budget movie Good Will Hunting, which he co-wrote and starred in with his friend Ben Affleck. The movie earned them an Oscar for original screenplay.

Early in his career, Damon enjoyed a reputation as a solid actor in films like The Talented Mr Ripley in 1999. He hit big at box offices with 2002 spy thriller The Bourne Identity and its 2004 follow-up The Bourne Supremacy. Other recent movie successes include Ocean's Eleven and Ocean's Twelve.