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.
The little prince represents a living link to Britain's imperial history -- the infant is the great-great-great-great-great-grandchild of Queen Victoria, who ruled at the peak of British power.
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 before giving birth, 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. That may be challenging in an age when the British royals are treated as major world celebrities.
Associated Press writer James Brooks in London contributed to this report.