Prince Charles spoke of his joy and pride in becoming a grandparent 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.
The media will now continue to camp outside the hospital to capture a similar photograph for William and Kate's son, who 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 the 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.
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 Queen Elizabeth II'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.