Prince William, who was present for the birth of the 8lbs 3oz (3.7kg) baby girl, brought his 21-month-old son to the hospital.
The Duke of Cambridge told the waiting crowds the couple were “very happy”.
It is the first time Prince George has been officially seen in public in the UK since he left the same hospital as a newborn in 2013.
Kate Middleton has given birth to a girl at 08:34 BST, Kensington Palace has announced.
The newborn princess is fourth in line to the throne.
Both Kate Middleton and her daughter are “doing well”, Kensington Palace said.
The name of the baby will be announced in due course.
Prince Charles, who had earlier said he was hoping for a granddaughter, and his wife Camilla said they were “absolutely delighted”.
Kate Middleton had been admitted to the private Lindo Wing at St Mary’s Hospital in Paddington, west London, at 06:00 BST.
The birth announcement came just after 11:00 BST.
The statement from Kensington Palace added: “The Queen, the Duke of Edinburgh, the Prince of Wales, the Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news.”
The newborn princess joins the line of succession behind her grandfather Prince Charles, father Prince William and brother Prince George, who was born at the same hospital in July 2013.
The princess is Queen Elizabeth II’s fifth great-grandchild.
Hundreds of well wishers have gathered outside St Mary’s Hospital to catch a first glimpse of the new princess.
There has been lots of speculation about a name from small girls in the crowd, from Disney-inspired Belle and Ariel to Alex, Stella and Rose.
A large number of journalists, photographers and broadcasters had gathered after the announcement that Kate Middleton was in labor.
Following the announcement of the birth, standing on the steps of the Lindo Wing, unofficial town crier Tony Appleton told crowds: “We welcome with humble duty the new baby of their Royal Highnesses the Duke and Duchess of Cambridge.
“The princess is fourth in line to the throne.”
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