The world gets its first glimpse of the new Prince. Photo: BBC

A formal bulletin confirming the birth of a baby boy has been displayed at Buckingham Palace. Photo: BBC News

Walking out to cheers from staff and well-wishers, Kate cradled her son and said it was "a special time".

Prince William said they were "still working on a name".

The couple then went back inside the private Lindo Wing and placed their son in a car seat. A few minutes later they came outside again and the duke drove his family home to Kensington Palace.

A small crowd had gathered outside the palace to greet them.

Speaking to reporters outside the hospital earlier, the couple both said the experience was "very emotional".

William and Kate appeared relaxed and smiled as they appeared on the steps of the hospital shortly before 19:15 BST in front of a mass of photographers.

Kate handed their baby, who was wrapped in a white shawl, over to her husband and the couple walked forward to speak to reporters.

Nappy change

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

"He's a big boy, he's quite heavy. We are still working on a name so we will have that as soon as we can."

He added: "It's the first time we have seen him really so we are having a proper chance to catch up."

A smiling duchess said: "It's such a special time. I think any parent will know what this feeling feels like."

Addressing the waiting crowd, Prince William said: "I'll remind him of his tardiness when he's a bit older.

"I know how long you've all been standing here so hopefully the hospital and you guys can all go back to normal now and we can go and look after him."

They also revealed William had done the first nappy change.

Earlier in the afternoon, the couple were visited at the hospital by the Prince of Wales and Duchess of Cornwall, and Kate's parents, Carole and Michael Middleton.

Prince Charles said the baby was "marvellous" while Mrs Middleton said he was "absolutely beautiful".

Speaking to reporters as she left the hospital, Mrs Middleton said: "We are so thrilled".

She added her first cuddle with her new grandson had been "amazing".

There has been no word yet on what the couple plan to name the prince and asked if she had been told or made any suggestions, Mrs Middleton said: "Absolutely not."

Prince William was at the hospital for the birth at 16:24 BST on Monday, and stayed with his wife and son, who weighed 8lb 6oz (3.8kg), overnight.

Kensington Palace said in a statement: "We would like to thank the staff at the Lindo Wing and the whole hospital for the tremendous care the three of us have received.

"We know it has been a very busy period for the hospital and we would like to thank everyone - staff, patients and visitors - for their understanding during this time."

The first public appearance of the royal baby attracted tweets from more than 18,000 people a minute, social network Twitter said.

But the figure was short of the peak of 25,300 tweets per minute on Monday night after his birth was announced, it said.

Meanwhile, the birth of the third in line to the throne was marked by gun salutes at Green Park and the Tower of London and the ringing of bells at Westminster Abbey.

And at Buckingham Palace, royal watchers and tourists queued in the rain to catch a glimpse of the bulletin announcing the arrival of the royal baby at 16:34 BST on Monday, which is being displayed on an easel.

The birth of the prince means the monarchy has three generations of heirs to the throne for the first time since 1894.

See previous story posted July 22, 2013:

Royal baby: Duchess Kate gives birth to baby boy

- Duchess of Cambridge gives birth to baby boy, Kensington Palace says

BBC NEWS

The Duchess of Cambridge has given birth to a baby boy, Kensington Palace has announced.

The baby was delivered at 16:24 BST at St Mary's Hospital in Paddington, west London, weighing 8lb 6oz.

The palace said in a statement that the duchess and the baby were "doing well" and would stay in hospital overnight.

The news has been displayed on an ornate easel in the forecourt of Buckingham Palace in line with tradition.

A bulletin - signed by the Queen's gynaecologist Marcus Setchell, who led the medical team that delivered the baby - was taken by a royal aide from St Mary's to the palace under police escort.

The document said: "Her Royal Highness, the Duchess of Cambridge was safely delivered of a son at 4.24pm today.

"Her Royal Highness and her child are both doing well."

The Kensington Palace press release said the Duke of Cambridge was present for the birth.

"The Queen, The Duke of Edinburgh, The Prince of Wales, The Duchess of Cornwall, Prince Harry and members of both families have been informed and are delighted with the news," it said.

And the Prince of Wales, in a separate statement, said he and the Duchess of Cornwall were "overjoyed at the arrival of my first grandchild.

"It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy," he added.

Grandparenthood is a unique moment in anyone's life, as countless kind people have told me in recent months, so I am enormously proud and happy to be a grandfather for the first time and we are eagerly looking forward to seeing the baby in the near future."

Prime Minister David Cameron said on Twitter: "I'm delighted for the Duke and Duchess now their son has been born. The whole country will celebrate. They'll make wonderful parents."

Deputy Prime Minister Nick Clegg said on Twitter: "Congratulations to The Duke and Duchess of Cambridge. Good news to make the whole country smile."

And Labour leader Ed Miliband, also writing on Twitter, said: "Many congratulations to the Duke and Duchess of Cambridge. I wish them and their son all happiness and good health."

Scottish First Minister Alex Salmond, meanwhile, said: "I am sure that people across Scotland will be absolutely thrilled to hear the news of the birth of a baby boy to the Royal couple and will want to join me in wishing the proud parents many congratulations."