The couple brought their son Prince George to the hospital to meet his new sister, and the family left together after Kate gave birth at 8.34am on 2 May.
The couple leaving the hospital together after the new baby was born on Saturday morning
The new princess of Cambridge
Kate and William wave to the crowd
Several of Sunday's newspaper front pages displayed the first pictures of the baby, who is fourth in line to the throne, with The Sun on Sunday and The Sunday Mirror opting for the same front page line of 'Sleeping Cutie':
The Duchess smiled as she presented her new daughter to the world, dressed in a yellow Jenny Packham dress. The designer is one of Kate's favourites and she is regularly seen in her gowns.
The new princess, who is still unnamed, was wrapped in a white shawl with a matching cap as she appeared to sleep in her mother's arms.
Prince George left the hospital with his babysitter, for a bath, it was reported, so did not appear with the rest of the family outside the hospital.