The baby girl was presented to the waiting cameras outside the Lindo Wing of St Mary's Hospital in London after a quick two-hour labour.
She then drove off with mum Kate and dad Prince William to spend her first night at her Kensington Palace residence nearby.
Charlotte has now emerged as the bookies favourite name for the new royal baby, edging closer to previous favourite Alice.
The other names doing the rounds include Olivia, Elizabeth and Diana, after the baby's late grandmother Princess Diana.
The princess, who is fourth in line to the throne, was delivered at 08:34 BST on Saturday and weighed in at 3.7kg.
The Duke and Duchess of Cambridge, meanwhile, will spend the next few days at Kensington Palace and are expected to travel to their country home Anmer Hall on the Queen's Sandringham estate in Norfolk.
The new princess will have the title of Her Royal Highness and has displaced uncle Prince Harry to become fourth is line to Britain's throne after her grandfather Prince Charles, father Prince William and brother Prince George.
For many it had been a long wait for the duchess to deliver - memorialised online as the "Great Kate Wait".
William is on six weeks unpaid leave from his new job as a helicopter pilot with East Anglian Air Ambulance, and will not resume training until June 1.
A Kensington Palace spokesperson declined to say just when Kate might return to full-time duties.
"With two young children under two, her focus will be on her family," he said.
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