The baby, their second child, weighed 8 lbs 3 oz and William was present at the birth, it said in a Twitter statement.
Her Royal Highness The Duchess of Cambridge was safely delivered of a daughter at 8.34am.
— The Prince and Princess of Wales (@KensingtonRoyal) May 2, 2015
The baby weighs 8lbs 3oz. The Duke of Cambridge was present for the birth.
— The Prince and Princess of Wales (@KensingtonRoyal) May 2, 2015
"Her Royal Highness and her child are both doing well," the palace added.
She gave birth at 8:34 am, some 2-1/2 hours after having been admitted in the early stages of labor to the private Lindo wing of St Mary's Hospital, West London, the palace said.
Both families of the couple had been informed, it said, including the new baby's great-grandmother Queen Elizabeth, her grandfather Prince Charles and William's brother Prince Harry.
A ceremonial town crier announced the birth of the new baby, who will be fourth in line to the throne after Charles, William and her older brother George.
No name for the newborn has yet been announced.
William, 32, was born at the same hospital to the late Princess Diana in 1982.
He and Kate, 33, met as students at St Andrews University in Scotland, married in a spectacular ceremony at Westminster Abbey in April 2011 and have since become global stars.
When Kate leaves hospital, the couple will initially return to Kensington Palace for a couple of days before heading to Anmer Hall, their country mansion on the queen's Sandringham estate in Norfolk, eastern England.
The much awaited birth of the second royal baby was celebrated across social media.
Check out the scene outside Kate's hospital http://t.co/5cgeUzPxsn #RoyalBaby pic.twitter.com/i2wM9QrOnD
— People (@people) May 2, 2015
Sixty five years after India became a republic, the number one trend on Twitter is #RoyalBaby.
— Sadanand Dhume (@dhume) May 2, 2015
The easel with the proclamation of the #RoyalBaby birth is up at Buckingham Palace! pic.twitter.com/xKBltwUPxn
— TODAY (@TODAYshow) May 2, 2015
https://twitter.com/SimpsonsQOTD/status/594462458510778368
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