The royal birth announcement said the boy was born at 4:24 p.m. weighing 8 pounds, 6 ounces. William was present for the birth, the statement said. The announcement did not include a name for the future monarch, though one is expected to be revealed in the coming days.
"Her Royal Highness and her child are both doing well and will remain in hospital overnight," it said. William issued a brief statement, saying "we could not be happier."
Cries of joy erupted from the waiting crowd amassed near Buckingham Palace as the news came through, and hundreds of onlookers some of whom had camped outside for hours crushed against the palace's fences to catch a glimpse of the bulletin formally announcing the birth placed outside the palace's forecourt.
"It's a crazy atmosphere, everyone is getting very excited," said Andrew Aitchison, 47, outside the palace. "It's great to be part of history, to say we were here and saw it all happen."
William's father, 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. "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."
William and Kate's son is expected to follow Charles and William to the throne.
The baby's gender had been of particular interest because the prospect of Kate's pregnancy had prompted a change to 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.