The television star, 40, and his 24-year-old fiancée have struggled to choose a name for their firstborn, but Peter finally announced the news on Monday – almost a month after the little tot was born.
"Ok FINALLY we have a name for our beaut of a baby girl," wrote Peter on his Twitter page and official website. "Ems, J, P and I have decided on Amelia :)))) So lovely fans before you read it anywhere else here it is. Love ya :)."
Just last weekend, the Mysterious Girl singer revealed that he and Emily had narrowed it down to four traditional monikers, with Amelia being "his favourite".
"We have four names. Maybe you can help me out actually," Pete told Jonathan Ross on his Friday night chat show. "We had Rose. I love Rose because it's English and beautiful.
"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."
Peter continued, "The baby came three weeks early. Then we looked at each other and I said, 'We haven't got a name,' so we started calling her Rose, but she wasn't a Rose."
"I believe in the institution of marriage but there's so many people who have been together with their partners twenty, thirty years and never got married and that's fine, that's perfect," said the father.
"In my case, I want to get married eventually, but I'm in no rush. What I wanted was the engagement. It's so important for me. She's got to finish her degree at the end of this year, then she'll be a fully qualified doctor. Let her do her F1, then we'll get married and then we'll have another baby."