The singer's wife Ayda Field gave birth to Theodora Rose Williams on Tuesday afternoon (September 18).
A message to fans on the star's official website read: "Praise be, it's Theodora Rose Williams, affectionately known as Teddy...born 3.33pm on 18.9.12, 7lbs 4oz...
"Baby, Mummy and Daddy are all rockin...Thank you for your best wishes...xxxx."
It had previously been claimed that the 'Candy' singer had pulled out of plans to be part of the Olympic Closing Ceremony in order to be with his wife in the later stages of her pregnancy.
He recently quipped that he had been feeling the effects of his wife's pregnancy almost as much as she had, saying: "I got fat. Isn't it incredible? She has to eat for two, but I've gained her weight.
"It must be the empathy. I read about it and it says that sometimes husbands suffer same effects during the pregnancy as their wife... if she was sick, I was. If she had bad mood, me too. This happened during the first three months."
Watch the video for Robbie Williams's new single 'Candy' below: