Updated at 3.49pm
The Duchess of Sussex gave birth to a baby boy on Monday, her husband announced on Monday.
Prince Harry said his wife Meghan Markle had given birth to a "healthy" baby boy and was doing fine.
"Both Meghan and the baby are doing well," he said. "We're still thinking about a name".
Buckingham Palace had announced that a royal baby was imminent early on Monday afternoon, saying "the Duchess went into labour in the early hours of this morning" and that an announcement would be made "soon".
Prince Harry and Meghan revealed they were expecting their first baby in October, at the outset of a 16-day tour of Australia, New Zealand, Fiji and Tonga.
Commentators at the time believed the baby, Queen Elizabeth II's eighth great-grandchild and seventh in line to the throne, was due in late April.
The 34-year-old prince and Meghan, 37, have reportedly opted for a home birth at their new Frogmore Cottage residence, on the grounds of Windsor Castle west of London.
Request for privacy
Buckingham Palace also said last month Prince Harry and Meghan wanted to keep the arrival of their first child "private".
That would also contrast with Prince William and Kate, whose newborns were immediately shown off by the couple in front of the world's media.
They have three children: five-year-old Prince George, Princess Charlotte, 4, and one-year-old Prince Louis.
Bookies' delight
As April came to an end without news of the birth, Britons have been on tenterhooks with royal-watchers eagerly awaiting the latest addition to the family.
Fans have already been seen gathering in Windsor as news that Meghan had gone into labour broke on Monday lunchtime.
There has been fevered speculation in recent weeks over everything from the newborn's gender and name -- to whether it will have Harry's ginger hair.
Punters have been betting heavily on the various options, with the favoured scenario that the baby will be a girl called Diana.
Other hotly tipped names included Ivy, Grace and Alice.
Some British bookmakers stopped taking bets last week on when the baby would be born, believing that it had already secretly arrived.
Breath of fresh air
Meghan was a popular US actress before marrying Prince Harry last May at Windsor Castle.
She has been hailed as a breath of fresh air in a stuffy institution.
Meghan, who grew up in California and is a long-time advocate of holistic treatments, has reportedly raised eyebrows during her pregnancy with some of her new-age ideals and US glitz.
How she intends to bring up the baby will only increase the scrutiny.