The Duke and Duchess of Cambridge have named their son George Alexander Louis, Kensington Palace has said.
The third in line to the throne, who was born on Monday at 16:24 BST, will be known as His Royal Highness Prince George of Cambridge.
The Queen was told of Prince George's name when she met him for the first time on Wednesday.
The family are at the Middleton home in Bucklebury, Berkshire, after spending a night at Kensington Palace.
George was the bookmakers' favourite for the first name of the prince.
The duke and duchess had been expected to pick a traditional royal name for their son, who was born at St Mary's Hospital in London, weighing 8lbs 6oz.
Royal infants usually have historical names which are passed down through the generations.
There have been six King Georges up to now, most recently the Queen's father, although his first name was Albert and he was known to his family as Bertie.
The name Louis is Prince William's fourth name and is likely to be a tribute to Lord Louis Mountbatten, the Duke of Edinburgh's uncle and the last British Viceroy of India before independence in 1947.
Prince Charles was immensely fond of his great-uncle Lord Mountbatten. Known by the Royal Family as Uncle Dickie, he was assassinated by the IRA in August 1979.
The prince's other middle name - Alexander - is one that three medieval Scottish kings have had, and was also the name of the famous 4th Century ruler Alexander the Great. The Queen's middle name is Alexandra.
BBC royal correspondent Nicholas Witchell said George will be seen as a tribute to the Queen's father but the couple are said to genuinely like the name themselves.
Alexander was a favourite of Catherine's, he added.
The BBC's Peter Hunt said Prince George does not have to be King George if he accedes to the throne - he can choose another name, as the Queen's father did.
"Royal names are diminishing. Edward VIII had 7; Prince Charles has 4; Prince William 4; Prince George 3. #princegeorge," he tweeted.
Charles Mosley, author of Blood Royal, told the BBC he knew it would be George.
"It was the name of the sovereigns under whom this country became a world player - in the 19th Century, defeating Napoleon, and in the 20th Century, winning two world wars.
"Louis is a nod in the direction of the Mountbatten element in the Royal Family. And indeed the surname of the royal family is still Mountbatten. His (Prince George's) birth certificate and marriage certificate will say Mountbatten-Windsor."
As well as being an established regal name, George is also a saint's name. St George was an early Christian martyr and is the patron saint of England.
The announcement of the new prince's name has been relatively quick compared with previous royal babies.
It was seven days before the name of a newborn Prince William was announced in 1982, and there was a wait of a month following Prince Charles's birth in 1948.
The Queen spent 30 minutes with her new great-grandson on Wednesday. At a reception at Buckingham Palace on Tuesday evening, the monarch said she was "thrilled" at the arrival of her third great-grandchild.
The Prince of Wales and Duchess of Cornwall, and Catherine's parents, Carole and Michael Middleton, paid visits to the hospital on Tuesday afternoon.
Later that day, Catherine's sister Pippa Middleton went to Kensington Palace and Prince Harry also paid his new nephew a visit.
The duke and duchess left Kensington Palace shortly after the Queen's visit and were driven to Bucklebury. It had been expected that the couple would want to spend time at the duchess's family home but it is not known how long they will stay.
Prince William has two weeks' paternity leave before he is due back to work in Anglesey where he is an RAF search and rescue pilot. (BBC)