Hundreds of Britons and tourists broke into song and dance outside the palace as officials announced that the future king was born at 4:24 p.m., weighing 8 pounds, 6 ounces, at central London's St. Mary's Hospital — the same place where William and his brother Harry were born three decades ago.
The imminent arrival of the royal baby was the subject of endless speculation on social media and was covered for days on live television around the world, but in the end the Royal Family managed to keep it a remarkably private affair.
In line with royal tradition, a terse statement announced only the time of birth, the infant's gender and that mother and child were doing well. It gave no information about the baby's name, and officials would say only that a name would be announced "in due course."
"Her Royal Highness and her child are both doing well and will remain in hospital overnight," it said. William also issued a brief statement, saying "we could not be happier."
Officials said William, who was by his wife's side during the birth, would also spend the night in the hospital.
William's press aides had talked about preserving Kate's "dignity" throughout the pregnancy, and the way the birth was handled showed that the palace's impressive stagecraft could give the royals a bubble of privacy even in the age of Twitter and 24-hour news broadcasts.
Just before 6 a.m., 31-year-old Kate, also known as the Duchess of Cambridge, entered the hospital through a side door, avoiding the mass of journalists camped outside. Officials did not announce she was hospitalized until more than an hour later.
Later, as the world media gathered outside filled hours of airtime with speculation, the baby's birth went unannounced for nearly four hours, allowing the royal couple the private time they needed to act like a regular family — a goal 31-year-old William has cherished.
He was able to tell his father, Prince Charles, and grandmother, the Queen, about the birth and enjoy his wife's company without having to cope with the overwhelming media and public desire for information.
By nightfall, the public still knew very few details, but most people seemed satisfied with the day's events. London's landmarks, including the London Eye, lit up in the national colours of red, white and blue, and the city had a party atmosphere unmatched since last summer's Olympics.
Outside the hospital, a man dressed as a town crier in traditional robes and an extravagant feathered hat shouted the news and rang a bell.
A car carrying the announcement drove from the hospital to the palace, where the news was greeted with shrieks of "It's a boy!" and strains of "For He's a Jolly Good Fellow." A large crowd rushed against the palace fences to catch a glimpse of an ornate, gilded easel displaying a small bulletin formally announcing the news.
The framed sheet of paper became the target of a thousand camera flashes as people thrust their smartphones through the railings. Hours after the initial announcement, crowds were still surging forward to get near the easel. Some placed presents and bouquets in front of the palace, while others waved Union Jack flags and partied on the streets to celebrate.
"It's a crazy atmosphere. Everyone is getting very excited," said Andrew Aitchison. "It's great to be part of history, to say we were here and saw it all happen."
More celebrations are expected Tuesday, including gun salutes by royal artillery companies to honour the birth. Riders in uniform will trot past the palace to Green Park, where six field guns will fire 41 blank rounds.
Charles and his wife, Camilla, spoke of their joy and pride in becoming grandparents for the first time.
"It is an incredibly special moment for William and Catherine and we are so thrilled for them on the birth of their baby boy," Prince Charles 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."
It could be some time before the baby's name is made public. When William was born, a week passed before his name was announced. Charles' name remained a mystery for an entire month.
The royal birth at St. Mary's Hospital recalled that of the baby's father, William, in 1982. Many remember the moment when he was carried out in Princess Diana's arms with proud father Prince Charles at their side.
William and Kate's son is third in line to the throne behind Charles and William.
The baby's gender had been of particular interest because the prospect of Kate's pregnancy had prompted a change in laws of succession to ensure that a daughter would not be passed over for the crown by a younger brother.
No one can tell what political and personal changes the intervening years will bring, but the baby can be expected to become the head of state of 16 countries, including Britain, Australia and Canada. The child will also eventually become Supreme Governor of the Church of England.
In Canada, the news of the birth was greeted with a flurry of congratulations.
Prime Minister Stephen Harper hailed the arrival of "a future sovereign of Canada," and said he's looking forward to seeing the son born to the Duke and Duchess of Cambridge.
Cian Horrobin, a spokesman for the Monarchist League, said the birth marked the beginning of a lifelong relationship for Canadians with "this boy who will one day be our king."
Even those opposed to the monarchy welcomed the prince's arrival.
Tom Freda, director of the organization Citizens for a Canadian Republic, said any news involving the Royal Family renews the debate over the relevance of a monarchist system, "and debate is good."
The little prince represents a living link to Britain's imperial history as the great-great-great-great-great-grandchild of Queen Victoria, who ruled at the peak of British power.
Many Britons had hoped that William and Kate would start a family shortly after their gala 2011 wedding, which drew a global television audience in the hundreds of millions.
The couple waited, however, until William was nearly finished with his military work as a search-and-rescue helicopter pilot based at an air base in a remote island off the coast of Wales.
That allowed Kate to ease into royal life, and to become more comfortable in the spotlight, before becoming a parent. It also allowed her to play a supporting role during the Queen's Diamond Jubilee celebrations last summer.
The first months of her pregnancy were not easy, and she was hospitalized in early December with acute morning sickness that left her weak and dehydrated. She seemed to recover her stamina fairly quickly and made a series of public appearances until the final weeks, drawing praise for her poise and good cheer.
The royal couple and their newborn are expected to spend much of their time in the coming years in renovated quarters at Kensington Palace, where William and Harry also spent much of their childhood.
Royal officials say Kate and William will try to give their child as normal an upbringing as possible, a challenging goal in an age when the British royals are treated as major world celebrities.
"He'll have to be protected all the time," said Edward Bentley, from near London. "But they'll make him seem normal and connected to the public for sure."
Associated Press writer James Brooks in London contributed to this report.