Introducing the child, who was wrapped in a white shawl, Meghan said: "He has the sweetest temperament, he's really calm. He's been the dream."
As they both laughed, Prince Harry said: "I don't know who he gets that from."
The couple confirmed they will introduce the Queen to her eighth and newest great-grandchild later on.
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."
Asked 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."
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.
Buckingham Palace said Harry was present for the birth, which is understood to have taken place in hospital as opposed to at home.
The baby will not automatically become a prince - although he could get that title if the Queen steps in.
Harry and Meghan might otherwise want him to inherit one of Harry's titles, such as Earl of Dumbarton, or they could reject any royal title at all.
The baby weighed 7lbs 3oz (3.2kg), making him lighter than each of his cousins.
Prince George was 8lb 6oz (3.8kg) when he was born in July 2013. His sister Princess Charlotte was 8lbs 3oz (3.7kg) when she arrived in May 2015, while their younger brother Prince Louis weighed 8lb 7oz (3.8kg) when he was born in April last year.
The average weight of a baby in the UK is about 7lb 7oz (3.4kg).
Credit: [BBC]Last modified on Wednesday, 08 May 2019