The baby girl, weighing 6lbs 1oz, was delivered at the Royal Cornwall Hospital in Truro at midday.
Speaking outside the hospital, Mr Cameron said:
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.
A Downing Streeet statement released earlier in the day said:
The Prime Minister and Mrs Cameron are delighted to announce the birth of their fourth child, a baby girl. Both the baby - who was born weighing 6lbs 1oz - and Mrs Cameron are doing very well.
The PM and Mrs Cameron would like to thank the doctors and nurses at the hospital for their help and kindness.
The Camerons’ child is only the third born to a serving prime minister since 1849.