"It's magic. It's pretty amazing," Meghan, 37, said as Harry, 34, held their son in his arms. "I have the two best guys in the world, so I'm really happy."
Meghan, who gave birth Monday at 5:26 a.m. local time, described the baby as "the dream."
"He has the sweetest temperament. He's really calm," said Meghan, prompting Harry to joke beside her, "I wonder who he gets that from."
"He's just been the dream, so it's been a special couple days," added Meghan, who was last seen in an official public appearance in March.
Harry and Meghan revealed the baby's name in an Instagram post later Wednesday. The post accompanied a photo showing Meghan holding the baby as she introduced Archie to his great-grandparents, Queen Elizabeth II and Prince Philip.
Also in the photo is Meghan's mother, Doria Ragland, who flew in from Los Angeles for the birth of her first grandchild and is staying with the couple at their Frogmore Cottage home.
Archie is the eighth great-grandchild for Queen Elizabeth and Prince Philip. They were the first members of the royal family to meet him.
Meghan said Wednesday that Archie first met Prince Philip when she and Harry "bumped into" him on their way to the photo call -- which came right before they were set to formally meet the great-grandparents.
"It'll be a nice moment to introduce the baby to more family," Meghan said. "And my mom is with us as well."
Meghan, wearing a sleeveless trench dress by designer Grace Wales Bonner, touched her son's head affectionately as she and Harry, who held the baby throughout the photo call, answered reporters' questions at Windsor Castle.
Archie wore a cashmere hat by G.H. Hurt & Son and was wrapped in an ivory white Leaves and Flowers Baby Shawl by the same brand.
The interview with the family of three took place inside St. George's Hall at Windsor Castle, the same venue for Harry and Meghan's wedding reception after their May 19 service in St George's Chapel.
When asked if Archie resembles mom or dad, Harry and Meghan said they are still "trying to figure that out."
"Everyone says that babies change so much over two weeks -- we're basically sort of monitoring how the changing process happens over this next month really," Harry said. "But his looks are changing every single day, so who knows."
Sporting a beard himself, Harry also joked, "He's already got a little bit of facial hair as well, wonderful."
"Parenting is amazing," Harry said. "It's only been, what, two-and-a-half days, three days? But we're just so thrilled to have our own little bundle of joy here to spend some precious times with him as he slowly starts to grow up."
The Duchess of Sussex gave birth to Archie at Portland Hospital, a private hospital in London, ABC News understands.
The birth announcement issued by Buckingham Palace indicated Meghan and Harry were home with their son at Frogmore Cottage just a few hours after the birth. Archie weighed 7 pounds, 3 ounces at birth, according to Buckingham Palace.
"We couldn't be more delighted at the news and we're looking forward to meeting the baby when we return," Charles said Tuesday while visiting Berlin with Camilla, the Duchess of Cornwall.
Prince William, who is in Wales with Kate, also sent congratulations to his brother, jokingly welcoming him Tuesday to the "sleep deprivation society."
"I'm very pleased and glad to welcome my own brother into the sleep deprivation society that is parenting," William, the father of three kids age 5 and under, said Tuesday as he and his wife, Kate, the Duchess of Cambridge, attended the King's Cup regatta in London. "[I'm] absolutely thrilled and obviously looking forward to seeing them in the next few days when things have quieted down."
Buckingham Palace has not commented on how much time Prince Harry and Meghan plan to take off after the birth of their first child.
Meghan took a moment Wednesday to thank people around the world for their support.
"Thank you every body for all the well wishes and the kindness," she said. "It just means so much."