Ahead of the birth, Harry and Meghan made a personal decision to keep their arrangements private, amid speculation that they had opted for a home birth at Frogmore Cottage, close to the Queen's Windsor Castle residence.
They also said they would only share the news of the baby's arrival once they had had a chance to celebrate privately as a family.
Baby Sussex's birth comes less than a year after Harry married American former actress Meghan in a glittering ceremony in St George's Chapel, Windsor Castle.
Harry, 34, and Meghan, 37, became engaged following a whirlwind 16-month romance after going on a blind date in London.
The duke had told how "all the stars were aligned" when they met.
News they were expecting a baby was announced in October at the start of the couple's busy 16-day tour to Australia, New Zealand, Fiji and Tonga.
Harry branded the baby "our little bump", while Meghan said they "were nearly there" in the final weeks of her pregnancy.
Unless the Queen steps in at the last minute, the baby will not be an HRH or a prince due to rules limiting titles within the royal family which were introduced by King George V more than 100 years ago.