Mr Cameron said "We are absolutely thrilled. She is an unbelievably beautiful girl. I am a very proud Dad. Both baby and Mum seem to be doing very well."
The newest Cameron addition, yet to be named, is only the second baby to be born to a serving Prime Minister in more than 150 years with the last being Tony and Cherie Blair whose son Leo who was born in 2000.
Congratulations to the whole Cameron family at this time of great joy.