05/17/2004 at 07:00 AM EDT
Gwyneth Paltrow and her husband Chris Martin have a new addition to their family: A baby girl named Apple Blythe Alison Martin, PEOPLE reported exclusively over the weekend.
The baby, weighing 9 lbs. 11 oz., arrived Friday at 1 a.m. after what a source close to Paltrow called "a long labor." Both mother and daughter are healthy and doing well in London, her publicist later announced.
By Sunday, well-wishers cheered them on and photographers snapped pictures as the proud parents strolled their London neighborhood with Apple cradled in Martin's arms. While the American actress and the British rocker have yet to explain why they chose the name Apple, the parents took the little girl's middle names from their respective mothers, actress Blythe Danner and Alison Martin.
"We are 900 miles over the moon," Martin told the BBC, "And we'd like to thank everyone at the hospital who have looked after us amazingly."
Coldplay, under the pseudonym The Nappies, recorded a special song about the birth and shot a video (featuring a rapping, bare-chested Martin) to go with it, both available for one week only on the Coldplay Web site.
Among the lyrics: "Sometimes you're happy, sometimes you frown/With your hormones bouncing up and down/Sometimes you're happy, sometimes you're sad/But the weird nine months that you have had."
The couple – who divide their time between London and Manhattan – announced Paltrow's pregnancy last Dec. 3, two days before the Shakespeare in Love
Oscar winner, 31, and the Coldplay frontman, 27, quietly became man and wife at a ceremony in Santa Barbara, Calif.