The father, Duke of Cambridge, was present at the birth of his daughter, who weighs 8 pounds 3 ounces (3.7 kg).The palace added that the mother and baby are "doing well". IN PICS: Celebrations begins as Kate gives birth to a baby girl
The new baby is fourth-in-line to the throne, behind her grandfather Prince Charles, father Prince William and brother Prince George.
The Duchess of Cambridge was earlier today admitted to the Lindo Wing of St Mary's Hospital in London, where her first baby Prince George was also born in July 2013, with early stages of labour.
Kensington Palace had made the announcement in the early hours of Saturday that the Duchess was driven to the hospital alongside her husband and later said the labour is "progressing as normally".
Kate was being looked after by consultant obstetrician Guy Thorpe-Beeston. He was joined in the delivery room by Alan Farthing, the Queen's surgeon-gynaecologist.There will be a traditional custom of placing a paper announcement outside Buckingham Palace of the new princess soon.
British Prime Minister David Cameron, who will be hoping for a baby bounce in the May 7 General Election which usually favours the ruling party, said: "One of the privileges of my job is you get to see them (Prince William and Kate) up front and they are a wonderful couple, they are loving parents.
"With the rest of the nation I'll be wishing them well on Saturday, hoping for a healthy and happy outcome."
The world's media began rushing to the media pen outside the hospital as the news of the labour was announced.
Unlike at the time of Prince George's birth, the world's press have been stopped from camping outside.
Fans of the royal family have also been gathering near the hospital with flags and banners in recent days with some sleeping in the rough in sleeping bags.
Royal protection officers, who carry concealed weapons at all times, were stationed at the Lindo Wing in anticipation of Queen Elizabeth II's newest great grandchild.
The father, Duke of Cambridge, was present at the birth of his daughter, who weighs 8 pounds 3 ounces (3.7 kg).The palace added that the mother and baby are "doing well".
IN PICS: Celebrations begins as Kate gives birth to a baby girl