Here is the low-down on the Duke and Duchess of Sussex's baby:
- When did the royal baby arrive?
Meghan gave birth at 5.26am on Monday May 6. It is believed she had a home birth at Frogmore Cottage.
- How was the birth announced?
In a palace statement, on the @SussexRoyal Instagram account and by proud father Harry himself, speaking at Windsor Castle's Royal Mews.
- What did Harry say?
The beaming duke said: "I'm very excited to announce that Meghan and myself had a baby boy earlier this morning, a very healthy boy.
"Mother and baby are doing incredibly well. It's been the most amazing experience I could ever have possibly imagined."
He paid tribute to his wife and added of his newborn son: "As every father and parent will ever say, you know, your baby is absolutely amazing, but this little thing is absolutely to-die-for, so I'm just over the moon."
The duke also revealed off camera that he had only had about two hours' sleep.
- What will the baby be called?
Harry said they have not decided yet.
"Still thinking about names. The baby is a little bit overdue so we've had a little bit of time to think about it," the duke said.
According to the bookmakers, Arthur, Philip, Albert, Alexander and James are among the favourites with punters.
But Harry and LA-born Meghan could break the royal mould and take inspiration from American traditions, or perhaps the former actress will follow the celebrity trend of picking an unusual first name.
- What will his title be?
The baby's title is expected to be Earl of Dumbarton - as the son of a duke, he is entitled to use one of Harry's lesser titles as a courtesy title.
Harry was made Earl of Dumbarton by the Queen on the morning of his wedding, as well as being given a dukedom.
Baby Sussex will one day inherit the title the Duke of Sussex from Harry.
His surname is expected to be Mountbatten-Windsor.
- Will the baby be a prince?
Not at this stage. He will not be a prince, nor an HRH, because George V limited titles within the royal family in 1917.
- Could the Queen make the baby a prince or a princess?
Yes. The Queen stepped in ahead of George's birth to issue a Letters Patent to ensure all the Cambridges' children would have fitting titles, but that was done well ahead of time and this royal baby is much further down the line of succession.
Under George V's rules, Harry and Meghan's son will eventually be entitled to be a prince when Charles becomes king, as the child of a son of a sovereign, but may decide not to use the title.
- When will we get see the baby?
In around two days' time, according to the duke.
"I think we will be seeing you guys in probably two days' time as planned as a family to be able to share it with you guys and so everyone can see the baby," he said.
- Who was told of the birth first of all?
Meghan's mother Doria Ragland was with Harry and Meghan at Frogmore Cottage.
The Queen, the Duke of Edinburgh, the Prince of Wales and the Duchess of Cornwall, and the Duke and Duchess of Cambridge were all told and are said to be delighted.
But touchingly, Harry's uncle and aunts - Lady Jane Fellowes, Lady Sarah McCorquodale and Earl Spencer - the siblings of his late mother Diana, Princess of Wales, were also among the first to know.
- Where does the baby fall in the line of succession?
Seventh in line. The baby has moved Harry's uncle, the Duke of York, down into eighth place in the line of succession.
Princesses Beatrice and Eugenie have shifted into ninth and 10th place, and the Earl of Wessex - the Queen's youngest son - has dropped out of the top 10 for the first time to 11th in line.
- How is the baby be related to the Queen?
The baby is a great-grandchild of the Queen and the Duke of Edinburgh - their eighth - and the Prince of Wales's fourth grandchild, the Duke and Duchess of Cambridge's niece or nephew, and a cousin for Prince George, Princess Charlotte and Prince Louis.
- Will he or she ever be monarch?
Unlikely. Future king George, plus Charlotte and Louis, are all further up the line of succession than Harry and Meghan's baby, so it is a safe bet that the throne will stay on the Cambridge side of the family in years to come.
- Will Harry and Meghan hire a nanny?
There have been rumours that Meghan will turn to her mother Doria for help initially.
But it is likely they will hire a nanny eventually, possibly an American one - or they are even reported to be considering a "manny" - a male nanny.
Harry has been close to all his nannies, especially Tiggy Legge-Bourke, and it is expected he and Meghan will arrange for a nanny to care for their baby while they are on official engagements.
Kate and William have the help of their full-time live-in nanny, Maria Teresa Turrion Borrallo.
Meghan's close friend, Jessica Mulroney, had two nannies to help her with her twin boys and younger daughter.
- Where will the baby live?
Harry and Meghan have set up home in Frogmore Cottage on the Windsor Estate.
It was gifted to them by the Queen and has undergone renovations costing taxpayers an estimated £3 million.
Will the baby have dual citizenship?
Harry and Meghan could apply for their child to have dual US-UK citizenship.
Meghan is planning to become a British citizen - but at present is still a US citizen.
According to the American Embassy in the UK, a child born outside the US and in wedlock to a US citizen parent and a non-US citizen parent may acquire US citizenship at birth if the US parent lived in America for five years - two of which were after the age of 14.
Will they be moving to Africa?
Plans are being made for the couple to spend an extended period abroad, possibly in Africa, as a way of harnessing their international appeal and expanding on their Commonwealth work.
A decision is unlikely to be taken until 2020, when they have settled down with their baby.
A Palace spokesman said the plans were speculative.