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.
It is thought the Queen was told of Prince George’s name when she met him for the first time on Wednesday.
The family are at the Middletons home in Bucklebury, Berkshire, after spending a night at Kensington Palace.
George was the bookmakers’ favorite for the first name of the prince.
Kate Middleton and Prince William 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.
Lord Louis Mountbatten and Prince William’s father the Prince of Wales were very close. Known by the Royal Family as Uncle Dickie, he was assassinated by the IRA in August 1979.
According to reports, Alexander was said to be a favorite of Kate Middleton’s.
The Queen’s middle name is Alexandra and it is assumed the baby has been named after the Queen’s father.
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.
Charles Mosley, author of Blood Royal, said 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.
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