Britain's Queen Elizabeth II paid a private visit on Wednesday to Prince William and his wife Kate to meet their newborn son, her great-grandson who will one day inherit the throne.

The 87-year-old spent just over half an hour at Kensington Palace in London where the still unnamed infant, the third in line to the throne, was spending his first day after leaving hospital.

The queen had said Tuesday she was "thrilled" about the latest addition to the family.

The Duke and Duchess of Cambridge revealed the new prince to the world on Tuesday when they left St Mary's Hospital in London to huge cheers and a roar from the international media massed outside.

Wearing a cornflower-blue polka-dot dress, a beaming Kate, 31, said the couple were "very emotional" following the birth of their first child on Monday.

William, also 31, said they were still choosing a name for the child dubbed Baby Cambridge and revealed he had already changed his first nappies.

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.

William's father Prince Charles and his wife Camilla, and Kate's parents Carole and Michael Middleton visited the hospital on Tuesday to meet their new grandson.

Wednesday's meeting was the first between the queen and her new heir, and 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 following exploratory surgery on his abdomen last month.

Outside the hospital, the baby had remained peaceful, seemingly oblivious to the deafening cheers from well-wishers and shouts from journalists who had camped for three weeks outside the hospital.

"It's a special time," said Kate. "I think any new parent would know what this feeling feels like."

Wearing jeans and a casual blue shirt, William told reporters: "He's got her looks, thankfully," as his wife laughed and interjected, "No, no, no, I'm not sure about that."

Their son was born at 4:24 pm (15:24 GMT) on Monday weighing a healthy eight pounds six ounces (3.8 kilogrammes), and William described him as "a big boy, he's quite heavy".

"He's got a good pair of lungs on him, that's for sure," William joked.

The prince is taking two weeks of paternity leave from his job as a Royal Air Force search-and-rescue helicopter pilot in Wales, and the couple 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 on Tuesday.

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.

After visiting the baby, first-time grandmother Carole Middleton had pronounced the baby "absolutely beautiful", while Charles said his grandson was "marvellous".

But they gave no clue as to what the couple will call their baby, with bookmakers favouring George and James as names fit for a king.

"We are still working on a name so we will have that as soon as we can," William said.

Under British law, the couple have up to 41 more days to register the birth of their child with local authorities -- for which they will need a name.

Royal tradition suggests there could be a wait ahead. William's name was not revealed until a week after his birth, while when Charles was born in 1948, the suspense went on an entire month.

The baby will be titled His Royal Highness, Prince (name) of Cambridge.

The first public appearance by the new family caused a storm on social media, with Twitter counting more than 18,000 tweets a minute -- a testament to the global fascination with the couple since their fairytale wedding in 2011.

The first photographs of Britain's new prince dominated newspaper front pages on Wednesday, with many noting the similarities between William and Kate's appearance and that of William's parents, Charles and Diana, following his birth at St Mary's in 1982.

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 princess, which also had a polka dot pattern.

Congratulations have poured in from around the globe for the baby, who is set to one day reign over Britain and 15 other countries including Australia, Canada and New Zealand.

Chinese fortune tellers predicted the baby will grow up to be determined but introverted -- and a big hit with the ladies. The child is born in the Chinese Year of the Snake, but is under the sign of Cancer in the western Zodiac.