The actress is about to turn 40

The baby was delivered on Sunday morning and named Coco Arquette.

The actress, who turned 40 on Tuesday, has struggled both on screen and in real life to have a baby, suffering a number of miscarriages in the past.

Cox and film actor David Arquette, who married in 1999, have spoken about their battle for a baby and said they would try IVF in an effort to conceive.

Cox is currently preparing for life without Friends with the sitcom ending after 10 seasons.

This year's episodes followed her character Monica's attempts to adopt a child.