She later gave birth to a “healthy” boy, Harry announced, adding that “this little thing is absolutely to die for”.
“The Duchess went into labour in the early hours of this morning,” the palace said in a statement, noting her husband the Duke of Sussex was by her side.
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, reportedly opted for a home birth at their new Frogmore Cottage residence, on the grounds of Windsor Castle west of London.
But it is unclear whether the first baby of the Duchess of Sussex, who is believed to be a week overdue, was being delivered at home.
The move would break with the tradition followed by Prince Harry’s brother William and his wife Kate, whose three children were all born in the private wing of St Mary’s Hospital in London.
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.
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 was 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 would 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.