The Duke and Duchess of Sussex have described him as having the "sweetest temperament".
Meghan and Harry could not hide their delight as they posed for pictures with the tiny infant in the majestic St George's Hall in Windsor Castle, just two days after he was born.
The duchess declared: "It's magic, it's pretty amazing. I have the two best guys in the world so I'm really happy."
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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."
Meghan added: "He's just been the dream so it's been a special couple of days."
The American former actress gave birth to the overdue 7lb 3oz boy on Monday at 5.26am.
The baby, whose name has not yet been announced, is seventh in line to the throne and the Queen and the Duke of Edinburgh's eighth great-grandchild and the Prince of Wales's fourth grandchild.
Amid surroundings steeped in royal history, the latest 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 delicate 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."
The couple, who are just 11 days away from their first wedding anniversary, were beside themselves with joy, giggling and looking into each other's eyes as they spoke.
The duke gently cradled his son in his arms and could not resist sneaking a peek down at him.
Meghan put her hand on the small of Harry's back as she listened to him talk.
The vast Hall at Windsor is where the duke and duchess gathered with family and friends for their daytime wedding reception last May.
The ornate ceiling is studded with the coats of arms of Knights of the Garter stretching back to 1348 and the walls feature figures of knights in armour.
Harry and Meghan are set to introduce their baby to the Queen, joined by Philip, in the castle's private apartments.