Both Catherine and her daughter are "doing well", Kensington Palace said. The princess weighing 3.7 kg is the fourth in line to the throne.
The Duke of Cambridge, who was present for the birth of the baby girl, brought his 21-month-old son Prince George to visit his sister.
The name of the baby hasn’t been announced yet.
British Prime Minister David Cameron has sent the best wishes to the royal couple on Twitter.
To mark the birth of the princess, a 21-gun salute will be fired in many places in London.