"It's magic, it's pretty amazing. I have the two best guys in the world so I'm really happy," Meghan said.
She added that the newborn prince "has the sweetest temperament" and is "really calm".
"He's just been the dream, so it's been a special couple of days," she said.
Harry cradled their son as reporters took pictures in St George's Hall at Windsor Castle, joking that he "already has a little bit of facial hair".
"We're so thrilled to have our own little bundle of joy," Harry said.
The new parents did not reveal the newborn's name until after visiting the queen earlier this afternoon. The Duchess of Sussex's mother, Doria Ragland, was also present.
Their son, who is seventh in line to the throne, was born at 5:26 a.m. on Monday and weighed 7 pounds, 3 ounces.
The royal couple confirmed the news of his birth via their official Instagram account.
In a video posted later that day, Prince Harry said his son's birth was "the most amazing experience I can ever possibly imagine".
"How any woman does what they do is beyond comprehension, but we're both absolutely thrilled," he said.
This is a developing story. Check back for updates.