The Duke and Duchess of Cambridge have named their daughter Charlotte Elizabeth Diana, Kensington Palace has said.
The fourth in line to the throne will be known as Her Royal Highness Princess Charlotte of Cambridge.
She was born on Saturday in the Lindo Wing of London's St Mary's Hospital weighing 8lbs 3oz (3.7kg).
The Queen and other senior royals were told of the baby's name before the announcement was made public.
The BBC's royal correspondent Peter Hunt said that a Kensington Palace official, when asked about the couple's choice of name, said: "We'll let the names speak for themselves."
Charlotte, the feminine form of Charles, has a long royal pedigree and became popular in the 18th Century when it was the name of George III's queen.
The King bought Buckingham House in 1761 for his wife Queen Charlotte to use as a family home close to St James's Palace - it became known as the Queen's House and is now Buckingham Palace.
Charles is the name of two former kings and of the Prince of Wales, the princess's grandfather.
Charlotte also has more recent connections for the royal couple.
On the duchess's side, it is the middle name of her sister Pippa Middleton and on the duke's it is the name of his cousin Charlotte Spencer, Earl Spencer's youngest daughter.
The earl tweeted: "Perfect names. My 2-year old Charlotte Diana will be thrilled at cousinly name-sharing."
According to figures from the Office for National Statistics, Charlotte is the 21st most popular girl's name in England and Wales with 2,242 babies being given it in 2013.
Elizabeth is 39th in the list but Diana is not in the top 100.
The duke and duchess and their daughter have been at home in Kensington Palace since leaving hospital on Saturday evening.
It is understood they will remain there for the time being before travelling to their country home, Anmer Hall, on the Queen's Sandringham estate, in Norfolk.
Royal historian Hugo Vickers said the choice of Charlotte as a name seemed to be based on taste rather than history.
"I don't think she is burdened by any history associated with it and to be honest I think they just chose the name because they liked it, which is what they do and what we respect about them.
"We historians can always find someone called Charlotte but I think basically they just liked the name."
Historian Dr Judith Rowbotham, of the University of Plymouth, said: "None of the Charlottes in the history of the British royal family have been lacking in character and personality, so one hopes that this one lives up to that name."
A family name
By Peter Hunt, BBC royal correspondent
Hard facts and royal pregnancies, labours and births are not natural bedfellows.
They represent a moment where the very personal, a couple celebrating the arrival of a daughter, collide with the very public - the father is a future king.
So, we don't know why William and Kate chose Charlotte as the first name of the fourth in line to the throne.
It conveniently has links to the Middletons, the present Windsors and past royals.
Elizabeth and Diana are more obvious choices.
Prince William has spoken of how, as he becomes older, his grandmother has become an even more important part of his life.
And it was inevitable that he would honour his mother and inevitable that he wouldn't "burden" his daughter with Diana as a first name.
As William said when he gave his fiancee his mother's engagement ring, it's a way of keeping her "close to it all".
Prime Minister David Cameron congratulated the duke and duchess on their new arrival and said he had "always liked the name Charlotte".
"It's a lovely name, and it must be such a precious time for this young couple," he said.
Earlier in the day gun salutes took place in London to mark the birth.
Soldiers from The King's Troop Royal Horse Artillery rode out in a procession from Wellington Barracks, near Buckingham Palace, to sound 41 shots in Hyde Park .
At the same time, the Honourable Artillery Company left their Armoury House barracks in the City of London to fire a 62-gun salute at the Tower of London.
A Kensington Palace spokesman said on Sunday: "The duke and duchess are hugely grateful for the messages of congratulations they have received from people all over the world.
"It means a great deal to them that so many people have celebrated the arrival of their new daughter."
The Prince of Wales and Duchess of Cornwall spent more than an hour with their new granddaughter. The duchess's parents, Michael and Carole Middleton, and sister Pippa also met the princess.
Prince Harry, who narrowly missed the princess's birth after returning to Australia to finish his secondment to the country's military, said his new niece was "absolutely beautiful" and he could not wait to meet her.