The new arrival will be named Coco Cox Arquette. Cox and actor husband David Arquette, became parents on Sunday morning.
The actress, who turns 40 today, gave birth about a week before her scheduled delivery date. She had checked into an undisclosed hospital on Saturday.
Cox, whose “Friends” TV character struggled to have a child, has disclosed that in real life she suffered several miscarriages before her successful pregnancy.
“I get pregnant pretty easily, but I have a hard time keeping them,” she said last October, revealing that she and her husband had decided to conceive by in-vitro fertilization.
The couple were married in June 1999.
Arquette, 32, has appeared in such films as “3,000 Miles to Graceland” and “Never Been Kissed.” He also appeared with his wife in all three “Scream” movies.
From working as a teenage model, Cox found her way to several commercial appearances.
Her big break, however, was rooted in director Brian De Palma’s decision to feature Cox as the girl pulled from the audience in Bruce Springsteen’s “Dancing in the Dark video.
Years later, after the actress had gained a great deal more notoriety, this short music-video appearance became a key piece of celebrity trivia in a multitude of magazines and entertainment shows.
In 1985, she starred alongside Dean Paul Martin in the forgettable series Misfits of Science and Cox reappeared on the television screen as Michael J. Fox’s girlfriend, psychology major Lauren Miller, in the 1980s sitcom Family Ties.
After co-starring with Jim Carrey in Ace Ventura: Pet Detective she won the role of Monica Gellar on the hugely successful sitcom Friends which screened its last episode in Ireland on Monday, May 24.