Cheering crowds rushed towards the gates of Buckingham Palace as it was announced that the Duchess of Cambridge had produced a healthy male heir weighing 8lbs 6oz (3.8 kilos).
The as-yet unnamed baby is third in line to the throne and in the direct line of succession after Queen Elizabeth II's eldest son and heir Prince Charles, and then his eldest son William.
"We could not be happier," William, the son of Charles and the late Princess Diana, said in a brief statement.
US President Barack Obama and his wife Michelle led international tributes to the "joyous occasion" while Canada was the first to hail the birth among the 15 overseas realms to which the baby will be heir.
The former Kate Middleton, 31, spent ten hours in labour after she and William went around dawn to the private Lindo wing of London's St Mary's Hospital, Paddington, in central London.
"Her Royal Highness The Duchess of Cambridge was safely delivered of a son at 4:24 pm (1524 GMT)," Kensington Palace said in a statement just over four hours after she gave birth.
"The baby weighs 8lbs 6oz. The Duke of Cambridge was present for the birth."
It was in the same hospital wing that the late Princess Diana gave birth to William in 1982.
Royal aides later placed a formal bulletin on a gold easel in the forecourt of Buckingham Palace which said that both Kate and her son were "doing well".
Kate, William and their new baby will remain in hospital overnight, the palace said.
The queen, 87, said she was "delighted" while Prince Charles said he was overjoyed.
British landmarks including the London Eye and BT Tower were lit in red white and blue to celebrate the baby's birth while cannon fire will ring out across the capital on Tuesday.
Newspapers splashed the arrival over their front pages, with many saying simply: "It's a boy."
The arrival of a royal baby and a new generation for the British monarchy has been hotly anticipated ever since the couple married in 2011 after a decade-long romance.
The popular couple have been widely credited with revitalising "The Firm", as the British royals are known, following decades of scandal and the death of Diana in a Paris car crash in 1997.
The palace said the boy's name would be revealed later, but he will be known as Prince of Cambridge.
Bookmakers say the favourites are George and James, traditional names for a future monarch -- although they had strongly backed a female child before the birth.
William, also 31, who was at his wife's bedside for the birth, has been on annual leave and will take two weeks' paternity leave from his job as a Royal Air Force search and rescue pilot.
The birth came later than widely expected, adding to the sense of anticipation -- as well as the frustrations of hundreds of international media who have waited outside the hospital for three weeks.
Prince Charles said that he and his second wife Camilla 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," the 64-year-old heir to the throne said in a statement.
"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."
The fact that it is a boy relieves the need to rush through new succession laws across the 16 Commonwealth realms, which would mean that a girl could no longer be overtaken by any future younger brothers.
Royal fanatics gathered in London could not hide their excitement.
"We think it's so exciting that there is a new third in line to the throne," said Janice, a visitor from Ohio in the United States. "We came here on Thursday and were very hopeful we would be here for the exciting news, we don't have royalty, so to us this is very very exciting."
The new arrival is Queen Elizabeth's third great-grandchild.
British Prime Minister David Cameron said outside his Downing Street office that it was "wonderful news" for Britain -- a nuclear-armed UN Security Council permanent member and the world's sixth biggest economy.
"It is an important moment in the life of our nation. A proud nation is celebrating with a very proud and happy couple tonight," Cameron said.
The Obamas said they wished William and Kate "all the happiness and blessings parenthood brings", adding: "The child enters the world at a time of promise and opportunity for our two nations."
The pregnancy was announced in December when Kate was admitted to hospital with severe morning sickness.
A pall fell over the proceedings when a nurse at the hospital committed suicide following a prank call by two Australian radio hosts pretending to be the queen and Prince Charles.