The first pictures of the Prime Minister’s daughter, who was delivered two weeks early by c-section weighing 6lb 1oz have been released today.
Mr Cameron said he was thrilled at the arrival of an “unbelievably beautiful girl”.
Mrs Cameron returned to the family’s holiday home from hospital with the newborn on Friday, where they will continue their break.
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.
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’s eldest son, Ivan, who suffered from cerebral palsy and severe epilepsy, died aged six last year.
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.