David Cameron described the birth of his fourth child as "a bit of a shock" today after wife Samantha gave birth early during their family holiday in Cornwall.
The baby girl, weighing 6lbs 1oz, was delivered by Caesarean section at the Royal Cornwall Hospital in Truro at midday. She had been due next month.
The Prime Minister said the baby was "unbelievably beautiful" and both she and Mrs Cameron were doing "very well".
"It was very exciting, we were on holiday, thought we were going to get through the holiday and then have a baby, and then it just seemed to kick off a bit quickly," he said.
"Samantha woke up this morning and thought she was having contractions and it was all beginning to get going, so we thought we would come to the hospital just to get everything checked out, and then things sort of sped up and it all happened very, very quickly and the baby popped out at about 12 o'clock."
He added: "It was a bit of a shock."
They went to the hospital at about 8am today after Mrs Cameron experienced "a couple of days" of contractions.
"We're absolutely thrilled. She is an unbelievably beautiful girl and I'm a very proud dad and both baby and mum seem to be doing very well, so it's really exciting," Mr Cameron said.
The Prime Minister said the baby did not have a name yet, but there would have to be a Cornish element.
Saying he was "in for suggestions" for names, he added: "It was very exciting having a baby in Cornwall, we'll have to have something Cornish in there somewhere.
"I've got the book out, Samantha's having a look through and she'll decide, I'm sure, before long."
His other two children were "thrilled, bouncing up and down, and dying to say hello to the new baby", he said.
Asked whether he and Samantha had decided on a name, he added: "No, not yet - not that I'll have any say in it, of course, anyway - but I think we will have to have something Cornish in the middle."
Mr and Mrs Cameron suffered tragedy last year when their elder son Ivan, who suffered from cerebral palsy and severe epilepsy, died aged six.
Their two other children are six-year-old Nancy and four-year-old Arthur Elwen.
The Tory leader hinted earlier this year that he wanted another child and news of his wife's pregnancy emerged just a few weeks before the general election was called for May 6.
Mr Cameron had been expected to return to work next week after the family's holiday, but he may now choose to take some paternity leave.
Deputy Prime Minister Nick Clegg, who has been holding the fort in Downing Street during the Camerons' holiday, sent his congratulations to the Prime Minister.
He said: "Miriam and I are absolutely delighted by the fantastic news.
"All our best wishes are with David and Samantha at this special time for them and their family."
The Camerons' new baby is only the third born to a serving prime minister since 1849.