'Mysterious Girl' singer Peter, 40, confirmed the name choice via Twitter on Monday afternoon (3 February), shortly after revealing in a TV interview that Amelia was his first choice.
Peter wrote: "Ok FINALLY we have a name for our beaut of a baby girl. Ems, J , P and I have decided on Amelia :):):) So lovely fans, before you read it anywhere else, here it is. Love ya ☺ (sic)."
J and P refers to his children Junior and Princess.
Trainee doctor Emily gave birth to the couple's first child on 7 January at Musgrove Park Hospital in Taunton, Somerset. Baby Amelia arrived three weeks earlier than planned. News of the birth was first leaked via Twitter on 9 January by fellow hospital visitors who claimed to have seen the famous couple in the vicinity.
Peter later confirmed the news via Twitter, writing: "Now that I have had the opportunity to tell Junior & Pringles, we are very happy to announce the safe arrival of our beautiful baby girl:) " he said. "We are extremely thrilled and mum and bubba are doing fine. We are looking forward to a nice quiet couple of weeks getting to know our baby (sic)."
Peter's message today confirmed what he'd previously told fans; that he and Emily had allowed his children Junior and Princess a say in choosing the name.
Tweeting last month, he said: "Haha she is a mysterious girl. No name yet. Still have time. Want the kids to help choose :)) (sic)."
Junior, eight, and Princess, six, are Peter's children from his marriage to ex-wife Katie Price.
Peter revealed during an interview on Jonathan Ross on Saturday night (1 February) that Amelia was his first choice for a baby name.
"We have four names. We had Rose. I love Rose because it's English and beautiful," Peter says. Amelia, beautiful name. Elizabeth. Alexandra. So these are the four names that we've been throwing around. I love them because they are English and they are beautiful."
He added: "I've got to consider, I've had two children, biological children, and this is [Emily's] first, so I want her to be happy. My favourite is Amelia. I love that name but I want her to be happy."
Well, it looks like Peter got his way – and Emily is happy! So good news all around!
Peter and Emily's relationship in pictures: