The couple's daughter, named Coco, was born Sunday morning, the spokeswoman for BWR Public Relations said. BWR represents both Cox Arquette and Arquette.
"Everyone's happy and healthy and that's what I have," the spokeswoman, who declined to give her name, told The Associated Press.
The actress, who turns 40 Tuesday, gave birth about a week before her scheduled delivery date.
Cox Arquette, 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 in October, revealing that she and her husband had decided to conceive by in-vitro fertilization (search).
The couple were wed in June 1999.
Arquette, 32, has appeared in such films as "3000 Miles to Graceland" and "Never Been Kissed." He also appeared with his wife in all three of the "Scream" movies.