The Duke and Duchess of Sussex have named their newborn son Archie Harrison Mountbatten-Windsor.
Introducing him to the cameras earlier in the day, Meghan said: "He has the sweetest temperament, he's really calm. He's been the dream."
As they laughed, Prince Harry said: "I don't know who he gets that from."
The announcement came after the Queen and Duke of Edinburgh met their eighth and newest great-grandchild for the first time at Windsor Castle.
By deciding to call their son Archie Harrison Mountbatten-Windsor, Harry and Meghan have chosen not to use a title for their first born.
As the first born son of a duke, Archie could have become Earl of Dumbarton - one of Harry's subsidiary titles - or have been Lord Archie Mountbatten-Windsor, but instead he will simply be Master Archie Mountbatten-Windsor.
BBC royal correspondent Jonny Dymond said it was a "strong indication that they don't want to bring him up as a formal 'royal'".
Talking about their first few days as parents, Meghan said: "It's magic, it's pretty amazing. I have the two best guys in the world so I'm really happy."
The duke added: "It's great. Parenting is amazing.
"It's only been two and a half days, three days, but we're just so thrilled to have our own little bundle of joy."
On which parent the baby resembled more, Harry said: "Everyone says that babies change so much over two weeks.
"We're basically monitoring how the changing process happens over this next month really. But his looks are changing every single day, so who knows."
Later, asked to show more of their son's face to the cameras, Meghan laughed as Harry joked: "He's already got a little bit of facial hair as well, wonderful."
Meghan added: "Thank you everybody for all the well-wishes and kindness, it just means so much."
A surprise choice, Archie was not among the bookmakers' favourites of Alexander, Arthur and Albert.
"I don't think anyone of us saw either of these names coming," says Joe Little, managing editor of Majesty royal magazine.
As far as he is aware, Archie does not have any British royal connotations - and Harrison too is a totally new name for the Royal Family.
Archie means "genuine", "bold" or "brave" - and is more popular in Britain than the US. It was originally a shortened form of Archibald but is now often used as a name on its own.
Pictures of the new family's first photocall were then shared on the SussexRoyal Instagram account.
"The Duke and Duchess of Sussex are delighted to share their first public moment as a family," the post said.
The images shared on social media were taken by Chris Allerton, who was the couple's private wedding party photographer, and took the picture of the newlyweds watching fireworks in the grounds of Frogmore House at their evening reception.
The infant, who is seventh in line to the throne, was delivered at 05:26 BST on Monday, with Harry saying after the birth that he and Meghan were "absolutely thrilled".
The Duke of Cambridge has welcomed his brother to "the sleep deprivation society that is parenting".
Prince William - a father-of-three - said he looked forward to seeing the new parents "when things have quietened down".
The Prince of Wales has also expressed his joy at the birth.
During an official visit to Germany with the Duchess of Cornwall, Prince Charles said: "We couldn't be more delighted at the news and we're looking forward to meeting the baby when we return."
A statement added that Meghan's mother, Doria Ragland, was "overjoyed at the arrival of her first grandchild" and was with her daughter at Frogmore Cottage - the new parents' home on the Windsor Estate.
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