The 'Candy' hitmaker - who has been sharing clips of Ayda Field's labour on his official YouTube account for the last 14 hours - spoke about his "astonishing" wife.
He said: "I've never been more in love, and I've never been more proud of my wife.
"She's been absolutely astonishing."
The baby, who 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.