"This will confirm that Oksana Grigorieva and Mel Gibson welcomed the arrival of a baby girl named Lucia on Friday, Oct. 30, 2009, at an undisclosed hospital in Los Angeles," says Gibson's rep, Alan Nierob, confirming earlier reports of the event. No further details were available.
"Everything is great! They couldn't be happier," a friend tells PEOPLE. "Everyone's healthy and thrilled. He loooves it!"
Gibson, 53, was at Grigorieva's side in Los Angeles until she and the baby went home from the hospital, then he flew to New York Sunday to resume shooting The Beaver, costarring Jodie Foster.
On Monday morning, an announcement of the birth was made on the set of the film in White Plains, N.Y. "Everyone sang '[For] He's a Jolly Good Fellow,' and he blushed," a member of the film crew told PEOPLE.
Gibson has seven children (six sons and a daughter) with his ex-wife Robyn, while Oksana, has a son, Alexander, with her former boyfriend, actor Timothy Dalton.
In April, Gibson's wife of 30 years, filed for divorce and later that month, he and Grigeorieva made their first public appearance together as a couple.
Their daughter's birth was first reported by Radar Online.