"It's magic, it's pretty amazing. I have the two best guys in the world so I'm really happy," she said.
Speaking in St George's Hall at Windsor Castle as her husband held their 2-day-old child, 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 couple left the photo call to introduce the baby to his great-grandparents, the Queen and Prince Philip.
The infant is the eighth great-grandchild of the Queen, 93, Britain's longest reigning monarch.
Meghan's mother, Doria Ragland, is staying with the couple at their Frogmore Cottage home near the Queen's Windsor Castle residence.
The baby is the first Anglo-American member of the royal family, and is eligible for US citizenship should his parents want it. He has African-American heritage through his mother.
Meghan, in a white dress, repeatedly rubbed her newborn's head as her husband in a light grey suit held their son. She described the days since her pregnancy as "special".
When asked who the baby most resembles, Harry said they would have to "monitor him over the next month" because "his looks are changing every day".
Both parents' smiles were palpable as they shared their baby with the world, as Harry described him as their "very own bundle of joy".