The world is eagerly awaiting the first glimpse of the Royal baby born to the Duke and Duchess of Cambridge.
The couple could leave hospital later with their son, whose name has not yet been revealed, and show the newborn prince to the world's waiting media and well-wishers.
The baby was born at 4.24pm on Monday weighing 8lb 6oz (3.798kg), with Prince William at his wife's bedside at the Lindo Wing of St Mary's Hospital in London.
Kensington Palace issued a very brief statement from the Duke who, speaking on behalf of himself and the Duchess, said: "We could not be happier."
William telephoned his family to tell them the good news, speaking personally to the Queen, his father Prince Charles and younger brother Prince Harry.
The Prince of Wales, who has become a grandfather for the first time, summed up the feelings of the Royal Family when he described the new arrival as an "incredibly special moment".
In a statement he 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."
A Buckingham Palace spokesman said: "The Queen and Duke of Edinburgh are delighted at the news."
News of the birth was issued in a statement by Kensington Palace at 8.30pm on Monday.
A spokesman added: "The names of the baby will be announced in due course."
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 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, who has developed a close relationship with the Queen, also spoke of their joy at the birth.
"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."
Various celebrations will be held later to mark the special occasion, including gun salutes across London.
The King's Troop Royal Horse Artillery and the Honourable Artillery Company will both carry out the ceremonial salutes in honour of the new addition to the Royal Family.
Gun salutes are fired for the birth of every prince or princess, no matter where their place is within the line of succession, the Ministry of Defence said.