The couple had chosen not to know the gender of their first child, who will be third in line to Britain's throne.
There has been widespread speculation over the birth of the Queen Elizabeth II's great-grandchild as Kate's exact due date had never been officially announced but expected to be mid-July.
The royal baby was delivered by a top medical team headed by the Queen's former gynaecologist Marcus Setchell, who delayed retirement after being asked by William and Kate to oversee the birth.