Boy Joy For Kate And William
The Duke of Cambridge was present for the birth of his son who weighed 8lbs 6oz. "We could not be happier," he said in a statement.
"Her Royal Highness and her child are both doing well and will remain in hospital overnight," Kensington Palace said in a statement.
"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."
The Prince of Wales said that he was "enormously proud and happy to be a grandfather for the first time", adding that it was "an incredibly special moment for William and Catherine".
In a touching statement, Charles said: "Both my wife and I are 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.
"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."
It is understood the Queen was informed of the birth in a phone call from William, though the Royal Family will not visit the hospital as it demands an extra level of security which could cause disruption.
Her Majesty arrived back at Buckingham Palace this afternoon after spending the weekend at Windsor Castle.
A beaming David Cameron declared the birth "an important moment in the life of our nation".
Speaking outside 10 Downing Street, the Prime Minister said: "It is wonderful news from St Mary's, Paddington and I am sure that right across the country, and indeed right across the Commonwealth, people will be celebrating and wishing the royal couple well.
"It is an important moment in the life of our nation but, I suppose, above all it is a wonderful moment for a warm and loving couple who have got a brand new baby boy.
"It has been a remarkable few years for our royal family - a royal wedding that captured people's hearts, that extraordinary and magnificent jubilee and now this royal birth - all from a family that has given this nation so much incredible service."
US President Barack Obama and his wife Michelle have congratulated the Duke and Duchess of Cambridge on the "joyous occasion of the birth of their first child", adding: "We wish them all the happiness and blessings parenthood brings.
"The child enters the world at a time of promise and opportunity for our two nations. Given the special relationship between us, the American people are pleased to join with the people of the United Kingdom as they celebrate the birth of the young prince.
"Given the special relationship between us, the American people are pleased to join with the people of the United Kingdom as they celebrate the birth of the young prince."
Confirmation of the Royal birth arrived by car in the form of an official statement, carried by the Duke and Duchess of Cambridge's press secretary.
The statement, on Buckingham Palace headed paper, was brought out for public inspection on the easel by Badar Azim, a footman with the Royal Household, and Ailsa Anderson, the Queen's press secretary.
It was signed by the Queen's gynaecologist Marcus Setchell, who led the medical team that delivered Kate's baby.
There were three cheers of "hip hip hooray," as the crowd outside the palace gates swelled to more than 10 deep.
Many had been waiting patiently for confirmation of the birth ever since news broke of the Duchess going into labour this morning.
Grown men were seen riding on friends' shoulders, while others used step ladders to get an elevated position.
Kasey Coffee, 21, from Washington in the US, said she had spent three hours queuing ahead of the royal announcement.
"The atmosphere in the crowd was awesome. Everybody was excited, then we heard a shriek that it was a boy - everybody was cheering and jumping. It was an incredible thing to be part of history."
Police were sent in with the crowds, as many scrambled to get the best vantage point.
But the wait to see the easel, designed to bring an end to a 12-hour vigil at the palace gates for some, proved too much.
One woman left having tried for half an hour to get closer to the front of the crowd, without success. She said: "I'm pleased we tried to see it, but it was just too difficult. It was impossible to get any closer."
Well-wishers from around the globe rejoiced as news of the birth of the royal baby spread.
Foreign Secretary William Hague said: "My warmest congratulations to the Duke and Duchess of Cambridge.
"Wonderful news and a happy moment for our country and Overseas Territories."
Canada's prime minister Stephen Harper sent his "heartfelt congratulations" to the couple and the royal family on behalf of all Canadians.
Outgoing Chief Rabbi Lord Sacks tweeted "Mazal Tov" to the happy couple. "We wish them blessings, good health, and joy in becoming parents," he added.
First Minister Alex Salmond led Scotland's congratulations to the Duke and Duchess of Cambridge on the birth of their baby son.
Mr Salmond 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."
Residents of the village where the Duchess of Cambridge grew up said tonight they were overjoyed with the news that one of their own is a future king.
John Haley, owner of the Old Boot Inn near the Duchess's parents' home in Bucklebury, Berkshire, said: "It's just amazing news. When we heard the announcement it was a boy, the place just exploded."
Mr Haley, who attended the royal wedding in 2011, added: "We are all having a massive party, it's a great atmosphere and it's all kicked off. It's great that Kate and her son are doing well."
The Duchess's former music teacher Daniel Nicholls, who taught her piano from 11 to 14 and who still lives near Bucklebury, said: "It's absolutely amazing news. I think they are going to be wonderful parents.
"I believe they are going to come here to the village with the child and I know that Kate's parents Michael and Carole will be a great support. Is he too young to start learning the piano? Maybe in the future..."
Tessy Ojo, CEO of the Diana Award scheme, an initiative which recognises teenagers who make outstanding contributions to their communities, spoke of Prince William's mother.
"Today Diana, Princess of Wales, would have been a proud grandmother," she said.
"Her legacy continues through the inspirational work of these young people who carry this honour, set up in her memory, with pride."
The new royal baby is third in line to the throne and a future king. A great-grandchild to the Queen - her third - the newborn will also one day be crowned sovereign.
If the baby follows after the Prince of Wales and the Duke of Cambridge as king, he will be the 43rd monarch since William the Conqueror obtained the crown of England.
The baby's uncle, Prince Harry, now moves to fourth in line to the throne, while the Duke of York shifts down to fifth and Princesses Beatrice and Eugenie to sixth and seventh place.