He said: "I've never been more in love, and I'venever been more proud of my wife. "She's been absolutely astonishing."
The baby - which has yet to be named - was born at 3.10pm on Monday and weighed 8 pounds, 2 ounces.
Robbie added: "The universe has presented itself to us again and it's been a very emotional, amazing few hours and we're really happy and honoured that you experienced the journey with us."
The 40-year-old singer - who married Ayda in 2010 - already has 2-year-old Theodora 'Teddy' Rose Williams with the actress.
Meanwhile, last month, it was revealed that Ayda was keen on a Los Angeles birth for their second child.
A friend of the couple previously said: ''The baby will be born in California for definite. Ayda did live in the UK with Robbie for almost a year after Teddy's birth but they're based in LA now.
''Ayda prefers living there as her friends and family are close by and she has a good support network.''
Robbie has been entertaining his fans today with amusing videos from the hospital room, including a video which showed him doing a rendition of 'Let It Go' from the hit movie, 'Frozen', whilst his wife appeared to be giving birth.
