David and Samantha Cameron have named their new baby daughter Florence Rose Endellion, Downing Street has announced.
Endellion refers to the Cornish village of St Endellion, close to where they are holidaying.
Downing Street said that the couple had received congratulatory messages from the Queen, the Prince of Wales, Gordon and Sarah Brown and French President Nicolas Sarkozy.
Mr Cameron spent the night at the Royal Cornwall Hospital in Truro where his new daughter was delivered by Caesarean section on Tuesday.
The couple's two elder children, six-year-old Nancy and four-year-old Arthur Elwen, have now visited their sister for the first time.