The news was greeted by huge cheers from the onlookers who had gathered outside the hospital and Buckingham Palace.
"Her Royal Highness The Duchess of Cambridge was safely delivered of a son at 4.24pm," said a statement from Kensington Palace. "The baby weighs 8lb 6oz.
"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. Her Royal Highness and her child are both doing well and will remain in hospital overnight."
The announcement of the royal birth was made via a press release sent out by Kensington Palace. The royal household made a last-minute change of plan to relay the news in this way first, rather than following royal tradition by making the announcement on an easel outside Buckingham Palace.
They did still announce the news on the easel, too, and excitement was at fever pitch when William and Kate's Press Secretary Ed Perkins appeared just after 8.30pm on the steps of the private Lindo Wing clutching a red leather folder containing the official document.
Written on Buckingham Palace-headed notepaper, the historic document had been signed by Kate's doctors Marcus Setchell and Alan Farthing.
The press secretary walked down the steps straight to a waiting car to deliver the precious declaration, which was then whisked to Buckingham Palace, arriving through the main gates with a police escort.
Following the happy announcement, Prince Charles expressed his pride and joy at becoming a grandfather for the very first time.
“Both my wife and I are overjoyed at the arrival of my first grandchild," the Prince of Wales said on Monday evening. "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."
Doctor Marcus Setchell, the Queen's former gynaecologist, has described the new arrival as a "wonderful baby, beautiful baby".
It remains to be seen what William and Kate decide to name their firstborn. Prince Charles and Princess Diana announced Prince William's name seven days after he was born, while Prince Harry's name was confirmed the day he left hospital.
The new royal baby will carry the title of His Royal Highness Prince of Cambridge.
On Monday, Britain awoke to the exciting news that Kate had been admitted to St Mary's Hospital in the early stages of labour. A royal convoy was spotted arriving at the hospital's rear entrance at around 6am, and at 7.30am Kensington Palace confirmed the news the world had been waiting for.
"Her Royal Highness The Duchess of Cambridge has been admitted this morning to St Mary’s Hospital, Paddington, London in the early stages of labour," the statement read. "The Duchess travelled by car from Kensington Palace to the Lindo Wing at St Mary’s Hospital with The Duke of Cambridge."
While the baby's due date was never announced, it is thought that the little Prince was around a week overdue.
The public will now excitedly await their first glimpse of the little newborn, and his delighted parents, who are expected to proudly introduce the baby boy to the world on the steps of the Lindo wing.
Watch all the action from outside the Lindo Wing as the world awaits news of the arrival of the Prince or Princess