Faith was born at the Centennial Medical Centre under a veil of secrecy, involving the celebrity couple booking out the entire top floor of the hospital and secretly entering the facility via a staff-only service elevator.
Kidman and Urban are Faith's biological parents. Initial reports had said the baby girl was born last week. Kidman and Urban released a statement thanking everyone for their support.
"Our family is truly blessed, and just so thankful, to have been given the gift of baby Faith Margaret," the couple said.
"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."
Kidman and Urban, both 43, were married in 2006 and have another daughter together, Sunday Rose, 2.
Kidman credited Sunday's unexpected appearance to swimming in the waters of a small Australian outback town during the filming of the film Australia.
She and six other women became pregnant after swimming in Kununurra.
Kidman and Urban probably deserve this year's best actress and actor Academy Awards for keeping Faith a secret.
Kidman has been on the hustings in the US, Australia and Europe undertaking numerous interviews to promote her latest project Rabbit Hole, a harrowing drama she produced and stars in as a mother dealing with the sudden death of a young son.
Urban has also sat through plenty of interviews.
And the pair made no mention of Faith yesterday when they attended the Golden Globe Awards in Los Angeles.
Kidman missed out on the Golden Globe best dramatic actress award for Rabbit Hole, with expectant mother Natalie Portman taking the gold statue for her performance in Black Swan.
Kidman has two adopted children with former husband Tom Cruise, 18-year-old daughter Isabella and 15-year-old son Connor, who live with Cruise in Los Angeles, but the teenagers are rarely seen in public with Kidman.
Kidman has hinted about her desire to have children and said in the latest issue of the US edition of Harper's Bazaar magazine that Isabella and Connor do not regularly visit her in Nashville.
"No, they don't," Kidman said.
"They're not crazy about Nashville. They're so grown up now. I mean, they're adults."
