The Prime Minister's daughter, who had been due next month, was delivered by caesarean section at the Royal Cornwall Hospital in Truro, weighing 6lb 1oz.
Mr Cameron said he was thrilled at the arrival of an "unbelievably beautiful girl".
She was driven from the rear of the hospital's maternity unit in a black-people carrier without waiting photographers, television cameras and reporters catching a glimpse of the new baby.
|Prime Minister David Cameron holds his baby daughter, Florence Rose Endellion |
The Prime Minister had been expected to be back at No 10 next week following his two week family holiday, but he will now take paternity leave.
Florence's middle name Endellion refers to the village of St Endellion on the north Cornish coast, near where the family were staying.
The couple's elder children, six-year-old Nancy and four-year-old Arthur Elwen, visited their sister while she was in hospital.
Mr and Mrs Cameron suffered tragedy last year when their son Ivan, who suffered from cerebral palsy and severe epilepsy, died aged six.
The Camerons' new baby is only the third to be born to a serving Prime Minister since 1849.
The Queen, the Pope and President Obama were among those who sent messages of congratulation to the Camerons.
The Prince of Wales, Gordon and Sarah Brown and French President Nicolas Sarkozy also sent their best wishes to the family.
- British PM Cameron does good job: 100-day poll 2010-08-18
- Cameron meets with Zardari in London 2010-08-07
- British PM David Cameron arrives Turkey for 2-day visit 2010-07-27