George, the patron saint of England, was the 12th most popular name in the UK in the past year.
The baby will be known as Prince George and as third in line to the throne will one day be king.
Kensington Palace said: "The Duke and Duchess of Cambridge are delighted to announce that they have named their son George Alexander Louis.
"The baby will be known as His Royal Highness Prince George of Cambridge."
Before the royal couple left the Lindo Wing of St Mary's Hospital in London where their baby was born, William revealed that naming the infant was a priority, saying: ''We're still working on a name, so we will have that as soon as we can.''
It had been thought the Duke and Duchess would spend a few days deliberating on what to call their son but it appears they may have had a name in mind and were discussing it with family members.
They followed tradition and picked names for their newborn which all have royal connotations.
Baby Prince George's other middle name - Alexander - is one that three medieval Scottish kings have had.
There have been six King Georges since the German-born George I, the first Hanoverian king of Great Britain, acceded to the throne in 1714.
The last was the Queen's father George VI who died in 1952 but was known to his family as Bertie.
George was the most popular name with the bookies with betting firms William Hill, Coral and Paddy Power all offering short odds on the moniker.
[Baby George: History of the royal newborn's name]
William Hill said that George had been by far and away the best backed boys name with the firm and ended as the 2/1 favourite ahead of James and Louis.
William Hill spokesman Joe Crilly said: "Yes, George has been incredibly popular with our punters in the last 24 to 48 hours but the pregnancy has lasted a lot longer than that and up until Monday the majority of the betting was for a girl .
"We are paying out a six figure sum to winning punters but the Royal Baby betting has been so popular that we have enough to get in a bottle of bubbly to wet the baby's head tonight."
Since the baby was born on Monday William Hill has taken 3,400 bets on the name George with 25 of those being three figure punts - the biggest was a £500 wager at 2/1 on Tuesday.
Mountbatten and William's father the Prince of Wales were very close, with Charles confiding in his relative.
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He was known by the Royal Family as Uncle Dickie and was assassinated by the IRA in August 1979.
His boat was blown up on a fishing trip off the coast of County Sligo, Republic of Ireland.