"Mother, son and father are all doing well this morning," a Kensington Palace Spokesman said.
"We would like to thank the staff at the Lindo Wing and the whole hospital for the tremendous care the three of us have received," a statement from the Duke and Duchess read.
The new family are expected to leave the hospital either after 6pm on Tuesday evening or on Wednesday morning.
The world's media remained camped outside the private wing of St Mary's Hospital, Paddington where Kate gave birth to the little Prince weighing 8lb 6oz at 4:24pm on Monday afternoon.
New parents Prince William and Kate Middleton celebrated the birth of their baby son with takeaway pizzas, according to reports.
After an undoubtedly tiring 11-hour labour, the future King's mother and father are said to have ordered two pizzas to the Lindo Wing of St Mary's Hospital, Paddington at around 8:45pm.
While the Duke and Duchess of Cambridge tucked into their pizzas, the news broke via email press release that their baby son had been born at 4:24pm that afternoon weighing 8lb 6oz...
Pizza is one of Prince William's childhood favourites. He and Prince Harry once forged a note asking the Kensington Palace chef Darren McGrady to "cancel the chicken and broccoli and cabbage tonight and give the boys pizza please.” The plot was instantly foiled when Darren recognised a seven-year-old's scrawly handwriting.
~ Hello! Magazine
Good for them! Pizza is always a fun choice!
Moments ago, Baby Cambridge's new grandparents, Kate's parents, were the very firsts vistors to see the new baby, which again, shows the significance of Kate's family in the lives of William and Kate:
Brand new grandparents Michael and Carole Middleton have arrived at St Mary's Hospital to meet their first grandchild. Kate Middleton's proud mother and father arrived at the Lindo Wing shortly after 3pm on Tuesday afternoon, less than 24 hours after their daughter welcomed a little boy.
About an hour later William's father and step-mother came to visit: