The 87-year-old monarch would have given final clearance for the name to ensure that it was in keeping with the traditions of the House of Windsor and a monarchy that has lasted more than 1,000 years.
Louis is one of William's middle names and was also the first name of Lord Louis Mountbatten, the Viceroy of India and a mentor to Prince Charles. Mountbatten was killed in an IRA bombing in the 1970s.
Bookmakers had George and James as the favourites.
The naming was relatively quick by royal standards. Charles and his first wife Diana took a week to announce William's name in 1982, while the world had to wait a month after Charles was born in 1948.
Under British law, parents have 42 days to register the birth - and the name - of their child. It is not clear whether William and Kate have officially done so yet.
The queen earlier spent just over half an hour at the palace, where the young couple spent the first night after leaving hospital with the baby, before she was driven away in a green Bentley limousine.
She has said she is "thrilled'' about the latest addition to the family, who will one day succeed her as head of state of Britain and monarch of 15 Commonwealth realms around the globe.
A few hours later, the Duke and Duchess of Cambridge took the little prince to stay with his maternal grandparents in the village of Bucklebury west of London, arriving in a convoy of four-by-four vehicles with police outriders.
Carole and Michael Middleton, self-made millionaires from a party goods business, visited the baby in hospital yesterday, where Kate's mother pronounced her first grandson "absolutely beautiful''.
Prince George's uncle Prince Harry - William's younger brother, who has been knocked down to fourth in line to the throne - and Kate's sister Pippa Middleton made separate visits to the couple at the palace.
"This is now private and quiet time for them to get to know their son,'' a palace spokesman said.
Royal aides said the couple had no immediate plans to hire a nanny, and Kate is expected to rely on her mother for support in the early weeks.
What's in a name?
The name George is synonymous with British kings.
It's come to represent the continuity of the monarchy and remained the bookmakers' favourite in the name-guessing stakes from the moment Kate's pregnancy was announced.
Six King Georges have worn the crown throughout history since the German-born George I, the first Hanoverian king of Great Britain, acceded to the throne in 1714.
The first name of the last King George - George VI - was actually Albert and he was known to his family as Bertie, but he selected George - his fourth name - to use as Sovereign.
He was the much-loved father of the present Queen and the new Prince George of Cambridge's great-great grandfather.
George VI chose George in honour of his father George V and to create the impression of stability after the scandal caused by the abdication of his brother Edward VIII.
George is also the fourth name of the Prince of Wales - the baby's grandfather. Even Edward VIII had George among his seven names.
The name means farmer or earth worker. It was the 12th most popular name for boys born in England and Wales in 2011.
St George, a fourth-century Christian martyr, is the patron Saint of England and represents honour, bravery and gallantry. The legend of George slaying a dragon and rescuing an innocent maiden is medieval.
There has only been one other Prince of Cambridge and he was also called George.
The first Prince George of Cambridge was a grandson of George III and the only son of Prince Adolphus Frederick, the 1st Duke of Cambridge.
- AP
