Social media networks were also abuzz with the news, which made headlines around the world.
'We could not be happier'
The new parents spent some time with their baby before calling family members -- starting with the queen -- to announce the birth, a Kensington Palace source told CNN royal correspondent Max Foster.
"We could not be happier," said Prince William, according to the Kensington Palace source.
Prince William remained at Catherine's side throughout the labor, and the baby was born naturally. An official bulletin was placed on a gilded easel outside Buckingham Palace.
The celebrations for the arrival of the new prince -- whose title will be His Royal Highness Prince (the baby's name) of Cambridge -- were hard to miss in the capital.
The fountains at Trafalgar Square were dyed blue; the BT Tower, a London landmark, flashed the words "It's a boy;" and the London Eye was illuminated in patriotic red, white and blue.
Farther afield, Canada -- where the British monarch is head of state -- turned its side of the Niagara Falls blue to mark the birth, and the CN Tower in Toronto was lit up the same color.
Betting on a name
It was a long wait for the media camped outside St. Mary's Hospital, but when the news of the birth finally came, the excitement of the moment was huge.
The Sun newspaper, Britain's best-selling tabloid daily, changed its masthead Tuesday to "The Son" to mark the occasion, above a picture of the official birth announcement, while the Daily Express and Telegraph emblazoned "It's a boy" across their front pages.
Recognizing that excitement over the prince's arrival is not universal, the Guardian newspaper's website lets users switch to a royal baby-free version of the home page. The front page of UK satirical magazine Private Eye simply says: "Woman has baby."
Many bets are being placed as the wait continues for the baby's name to be announced. British bookmakers Ladbrokes have James as favorite, followed by Henry and George, Philip, Alexander and Richard.
William's name was announced a few days after birth; his brother Harry's on departure from hospital.
Some British parents have delayed naming their newborns in recent days in hopes of either copying or avoiding the royal name, he said.
The official British Monarchy Twitter feed said: "The Queen and Prince Philip are delighted at the news of the birth of The Duke and Duchess of Cambridge's baby."
Charles Spencer, brother of the late Diana, Princess of Wales, welcomed the birth of the baby. "We're all so pleased: it's wonderful news," he said in a statement.
"My father always told us how Diana was born on just such a blisteringly hot day, at Sandringham, in July 1961. It's another very happy summer's day, half a century on."
British Prime Minister David Cameron said, "It is an important moment in the life of our nation, but I suppose above all, it's a wonderful moment for a warm and loving couple who got a brand new baby boy."