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The Angels singer and his wife, Ayda, welcomed daughter Theodora Rose into the world on Tuesday and the tot - who will be known as Teddy - weighed in at just over 3kg.
Both mother and baby are doing well.
He wrote on his official blog: "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 (sic)"
Traditional moniker
Robbie recently revealed the couple had chosen a name for their daughter and was pleased it was a traditional moniker.
He said: "Right now I'm ecstatic. We do have a name but we're not going to get it out in case it gets tweeted.
"And as a celebrity we're supposed to call them Aubergine or something like that aren't we?
"I do have a sort of celebrity name but it's not Appleesque. It's a very solid, old-school name."
Robbie also said he is planning to move back to England from Los Angeles because he doesn't want his daughter to go to school with the "fucking idiots" in the city although he admitted he and American born Ayda are still discussing their future living arrangements.
'They are idiots in LA schools'
He said: "I don't want to educate our baby in LA because I would much prefer her to have English sensibilities.
''They are idiots in LA schools. They are fucking idiots. They are a breed of idiots that only exist in Los Angeles and she would be surrounded by them. It's not like one or two either. It's not like the Big Brother house, where you pick the worst ones.
"I think kids there have a massive sense of entitlement, are dull and dumb. It means me coming back to the UK for good but I can live with that. It's worth being pestered for her to have a good school.
"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."
