The duchess and her husband Prince William welcomed their new daughter at 8.34am, Kensington Palace has confirmed.
The baby weighs 8lbs 3oz, and both mother and daughter are said to be doing well.
According to official tweets, The Duke of Cambridge was present for the birth and The Queen, The Duke of Edinburgh, The Prince of Wales & The Duchess of Cornwall, Prince Harry and members of both families have been informed of the birth.
Unofficial Town Crier Tony Appleton announced the news to the masses of people gathered outside the Lindo Wing at St Mary's Hospital.
Prime Minister David Cameron has congratulated the couple on Twitter, and said he was delighted to hear the news.
Congratulations to the Duke and Duchess of Cambridge on the birth of their baby girl. I'm absolutely delighted for them.
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— David Cameron (@David_Cameron) May 2, 2015
Nick Clegg and Ed Miliband also congratulated the couple on social media.
Prince William took the couple's son George to the hospital this afternoon to meet his new sister for the first time.
Prince George waves as he is taken into the Lindo Wing by The Duke of Cambridge to meet his little sister pic.twitter.com/Q9LUbY6k8j
— Kensington Palace (@KensingtonRoyal) May 2, 2015
William and Kate were admitted to the Lindo Wing at St Mary's Hospital in Paddington, Central London at 6am on Saturday (May 2) when the duchess was said to be "in the early stages of labour".
The duke and duchess had arranged a special delivery of cake and coffee on Tuesday morning (April 28) for well-wishers gathered outside the hospital.
The duke and duchess are already parents to Prince George, who was born in July 2013.
The new baby is fourth in line to the throne behind Prince Charles, Prince William and 21-month-old George.
Tasha is a freelance writer for with a particular interest in the representation of women in film and TV. After graduating with a Literature degree then journalism qualifications with News Associates a few years further back than she’d like to admit, Tasha began her freelance career. She’s worked as a writer, editor and commissioning editor for a number of publications including Digital Spy. She is also a theatre critic. LinkedIn
