George was the bookmakers' clear favourite for the third-in-line to the throne as it pays apparent tribute to Queen Elizabeth II's father King George VI, the infant's great-great-grandfather, who died in 1952.
"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," Kensington Palace said in a statement.
The baby will not automatically be King George VII whenever he comes to the throne, however, as there have been reports that William's father Prince Charles may take that title when he becomes king.
The announcement came just hours after the queen visited William and Kate at Kensington Palace, their London residence, and met her newborn great-grandson for the first time.
In this Tuesday, July 23 file photo, Kate, the Duchess of Cambridge, carries her new born son, the Prince of Cambridge. (AP Photo)
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.
A file picture taken on July 23 shows Catherine, Duchess of Cambridge, (L) and Prince William posing for pictures with their new baby son. (AFP Photo)
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 on Tuesday, 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.
William is taking two weeks of paternity leave from his job as a Royal Air Force search-and-rescue pilot, and the couple, both 31, are expected to take some time away from the cameras.
"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.
Echoes of William's own birth
The new baby was revealed to the world when the royal couple left St Mary's Hospital in London on Tuesday evening to huge cheers from the international media massed outside.
When the queen met her new heir on Wednesday, she became the first British monarch to meet a third-generation direct heir since Queen Victoria a century ago.
The monarch, wearing a turquoise floral outfit, made the visit without her husband Prince Philip, 92, who is convalescing after exploratory surgery on his abdomen last month.
The queen's private visit -- she was quickly whisked in and out of the palace -- contrasted with William and Kate's highly public outing on Tuesday.
Wearing a cornflower-blue polka-dot dress as she emerged from the private Lindo wing of the hospital, a beaming Kate said the couple were feeling "very emotional" and that it was a "special time".
The baby behaved impeccably, raising a tiny hand above his white blankets -- his first royal wave of a lifetime that will be spent in the public eye.
"He's got a good pair of lungs on him, that's for sure," William joked, adding: "We are still working on a name so we will have that as soon as we can."
British newspapers noted the similarities between William and Kate's appearance and that of Charles and Diana following William's birth at the same hospital.
Kate was wearing the sapphire engagement ring that belonged to Diana, while her empire-line dress, a bespoke design by Jenny Packham, also drew strong comparisons with that worn three decades ago by the late princess, which also had a polka-dot pattern.
Congratulations have poured in from around the world, while Chinese fortune tellers predicted the baby will grow up to be determined but introverted – and a big hit with the ladies.