The Aussie couple's baby was born via a surrogate in their adopted Nashville, Tennessee on 28 December (10), according to reports.
Urban and Kidman, who reportedly booked out the entire top floor of Nashville's Centennial Medical Center so the unnamed birth mother could deliver the child in secret, have named the little girl Faith Margaret.
The pair made no mention of the baby when they attended the Golden Globe Awards together in Los Angeles on Sunday (16Jan11), but released a statement on Monday (17Jan11), which read, "Our family is truly blessed, and just so thankful, to have been given the gift of baby Faith Margaret.
"No words can adequately convey the incredible gratitude that we feel for everyone who was so supportive throughout this process, in particular our gestational carrier."
The couple has a daughter, Sunday Rose, who was born in 2008. Kidman also has two adopted children, both teenagers, from her marriage to Tom Cruise.