The Duke and Duchess of Cambridge have announced that their baby son will be called Prince George of Cambridge.

The full name for William and Kate's newborn is George Alexander Louis - three names that all have strong royal connections.

George has come to represent the continuity of the monarchy and was the bookmakers' favourite from the moment the Duchess' pregnancy became public.

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.

If the Prince of Wales and William choose to use their first names when they become monarchs, and not a middle name, the infant prince will one day become King George VII.

The baby prince's name is likely to be in tribute to the Queen's father, and the infant's great-great grandfather, King George VI. The monarch's grandfather also had the same name - King George V.

The Queen saw her great-grandson for the first time yesterday morning, when she visited the Duke and Duchess at their home at Kensington Palace, and may have learned of their final choice of moniker at the meeting.

Historian and biographer Robert Lacey said: "George is obviously a tribute to the Queen's father and will, I imagine, give Her Majesty great pleasure."

Before the royal couple left the Lindo Wing of St Mary's Hospital in London where their baby was born on Monday, William revealed that naming the infant, who is third-in-line to the throne, was a priority, saying: ''We're still working on a name, so we will have that as soon as we can.''

The couple are understood to have had a few ideas for names in mind but it took a couple days for them to finally confirm which one was right for their son.

It was William and Kate's decision what to call their firstborn, and all three names were chosen because they liked them.

Kensington Palace issued a short statement telling the world of the couple's decision: "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."

The name Louis could be another tribute to a Royal Family member - the important figure of Lord Louis Mountbatten, the Duke of Edinburgh's uncle and the last British Viceroy of India before independence in 1947.

Mountbatten and William's father Charles were very close but Uncle Dickie, as he was known in the family, 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.

Baby Prince George's other middle name - Alexander - is one that three medieval Scottish kings have had, and was also the name of the famous ruler Alexander the Great.

William's step-mother the Duchess of Cornwall has a three-year-old grandson called Louis - born to her daughter Laura Lopes and husband Harry.

William and Kate left their Kensington Palace home yesterday for the Berkshire village of Bucklebury and the family support of Michael and Carole Middleton, who have already described their grandson as ''absolutely beautiful''.

With the Duke on two weeks' paternity leave and the Duchess receiving help from her mother, the royal couple will have the time to relax and get to know their son.

After the excitement of the infant's first public appearance outside St Mary's Hospital in Paddington on Tuesday, a Kensington Palace spokesman stressed that the Cambridges were now focused on the age-old job of caring for their baby.

He said: ''This is now private and quiet time for them to get to know their son.''

Bookies Paddy Power said it paid out £250,000 to punters who put money on long-standing favourite George to be the name of the royal baby.

One lucky customer put £2,000 on the name, which was priced at 5/2, and walked away with more than £5,000.

Rory Scott, from Paddy Power, said: "Kate and Wills have put us out of our misery at last and pleased the punters by picking the favourite - it's quite right we should be paying out a princely sum."

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