Kate, 33, gave birth to the fourth-in-line to the throne at 8.34am at the private Lindo Wing at St. Mary's Hospital in Paddington, London, on Saturday 02 May.
She weighed 8lbs 3oz, but a name has not yet been announced.
Keen to get home after welcoming their new baby, Kate and William emerged from the hospital to the glare of cameras from around the world at 6.10pm.
Kate looked beautiful in a yellow and white flowered dress, while the unnamed baby girl was dressed in white and fast asleep. Awwwwww!
The Duke and Duchess posed for photographs, before putting their newborn daughter into a car seat and driving to Kensington Palace for at least one night.
The couple will then head to their Norfolk home and family life as four.
Although they did not speak to the waiting press, they did release a statement via Kensington Palace's Twitter page.
It said: "Their Royal Highnesses would like to thank all staff at the hospital for the care and treatment they have all received.
"They would also like to thank everyone for their warm wishes."
Speculation that the couple were preparing to leave hospital has been rife since Kate gave birth this morning.
Dedicated fans have been waiting outside the hospital for a glimpse of the newborn, and were earlier rewarded with their efforts when the Duke of Cambridge brought George to be introduced to his baby sister.
It was a rare glimpse of the Prince - who was being looked after by Kate's mum Carole during Kate's labour - and, after waving at waiting photographers and fans, he spent around 45 minutes with his new sister.
Kate and Wills' departure came a few hours after Prince William's father Prince Charles and Camilla, the Duchess of Cornwall, offered their congratulations.
They said: "We are absolutely delighted by the news."
During an engagement at Windsor Castle earlier this week, 66-year-old Charles revealed that he and the Duchess of Cornwall, were "hoping for a granddaughter".
The birth was announced on Saturday morning via Twitter and email.
Traditionally a royal birth is announced in the following way: the medical staff sign an official birth announcement that is taken by a royal aide - via police escort - to Buckingham Palace where it is attached to an easel for the public to see.
The easel remains in place for 24 hours, so that well-wishers can get a look at the historic notice.
Although the famous baby's name has not yet been announced, Alice and Charlotte are hotly tipped favourites. Elizabeth, Victoria, Grace and Diana are also popular predictions.
For exclusive competitions and amazing prizes visit Reveal's Facebook page NOW!