The boy - whose name is yet to be announced - came under the spotlight early this afternoon, as the royal couple posed for pictures with their new arrival in St George’s Hall at Windsor Castle.
“It’s magic, it’s pretty amazing. I have the two best guys in the world so I’m really happy,” Meghan told the media.
As her husband held their son, Meghan added: “He has the sweetest temperament, he’s really calm.”
As they both laughed, Harry said: “I don’t know who he gets that from.”
The royal baby made his debut behind closed doors, with a small press pool of only one reporter, one photographer, three cameramen, as well as the couple’s own private photographer and a household press officer photographer.
Asked who the baby takes after, Meghan said: “We’re still trying to figure that out.”
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.”
Baby Sussex was sleeping soundly, wrapped in a white blanket and wearing a white knitted hat.
Asked how he was finding parenting, Harry said: “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.”
Harry said they were looking forward to spending some “precious times with him as he slowly, slowly starts to grow up.”
Asked about going to see the Queen and the Duke of Edinburgh, Meghan said: “We just bumped into the duke as we were walking by, which was so nice.
“So it’ll be a nice moment to introduce the baby to more family, and my mum’s with us as well.”
Harry added: “Another great-grandchild.”
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.”
Prince Harry, the Duke of Sussex, had announced his son’s arrival on Monday outside his Windsor home, Frogmore Cottage.
“Mother and baby are doing incredibly well,” he said.
“It’s been the most amazing experience I could ever have possibly imagined. How any woman does what they do is beyond comprehension.”
The two-day-old weighed 7lb 3oz and is the Queen’s eighth great-grandchild.