The 38-year-old Take That star took to Twitter to announce that wife Ayda Field had given birth to a baby girl.
Writing on his blog on Tuesday, he said: "Praise be, it's Theodora Rose Williams, affectionately known as Teddy..... Born 3.33pm on 18.9.12, 7Ibs 4OZ.
"Baby, Mummy and Daddy are all rockin.... Thank you for your best wishes XXXX."
Williams and his US actress wife recently announced that they had chosen a traditional name for their daughter, adding there was going to be "No mad celebrity baby name".
"I do have a sort of celebrity name but it's not Appleesque," he said. "It's a very solid, old-school name."
The singer also expressed concern last week that he may miss the London birth while touring in other parts of the UK but said he had a private jet on standby.
"There's a plane on standby and if I get that phone call I've got to go," he said.
Williams has said that he would prefer his child to grow up in the UK instead of Los Angeles, where the couple currently live.
He described children educated in LA schools as having "a massive sense of entitlement and that they were "dull and dumb".
"I don't want to educate our baby in LA because I would much prefer her to have English sensibilities.
"I want the baby to have an English passport, we're still figuring out exactly whereabouts the baby is going to be brought up.
"I had a conversation with the wife last night about where we're going to end up but we still don't know."
Williams and Field, a Turkish American actress, have been in a relationship for five years.
It is the first child for the couple who married two years ago.
Congratulations poured in on Twitter with well wishers praising the name of the child.
Williams rose to fame in the 1990s with the boy band Take That but has had more commercial success as a solo artist, becoming one of UK best-selling singers.
Last week he launched his new clothing line
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