Meghan said: "It's pretty amazing and I have the two best guys in the world so I'm really happy. He has the sweetest temperament, he's really calm. He's just been a dream, it's been a special couple of days."
Meghan, 37, and Harry, 34, will be introducing their son to the prince's grandparents Queen Elizabeth II and Prince Philip this afternoon.
Meghan's mother Doria Ragland will also be there for the special moment.
The former actress - previously known as Meghan Markle - said: "It will be a nice moment to introduce the baby to my family, my mom's with us as well."
Harry cradled his newborn son throughout the unveiling and admitted it is hard to tell who the baby looks like yet.
The prince - whose parents are Prince Charles and the late Princess Diana - said: "Everybody says that babies change so much over two weeks so we'll be monitoring the changing process over this next month really. His looks are changing every single day.
"Parenting is amazing, it's only been two-and-half days, three days, but we're just so thrilled to have our own little bundle of joy and share some precious times with him as he slowly starts to grow up."
The couple did not make an announcement as to what they are naming their son but that is expected to come after the queen has met her eighth great-grandchild.
Alexander, Arthur and James are among the favourite names with bookmakers.