Introducing him to the cameras earlier in the day, Meghan said: "He has the sweetest temperament, he's really calm".
The Duchess said it had "been a special couple of days" and thanked well-wishers for the outpouring of support they had received.
The seventh-in-line to the throne, who was born at 05:26am on 6 May 2019, hasn't yet had his title revealed.
In January, The Sun reported that Prince George told a dog walker that his name is Archie, when he was out with his grandmother Carole Middleton and sister Princess Charlotte in Berkshire. He added that "parenting is awesome".
"Parenting is incredible, 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". Meghan appeared to be in excellent health when she and Prince Harry appeared in Windsor Castle with baby Archie and answered press questions.
It's a decision that suggests Meghan and Harry want to give their son as normal a life as possible. "It's been the most wonderful experience I could ever have possibly imagined".
The first photos of Baby Sussex are here.
He shares a name with a character who is part of the Archie gang, along with a host of others - including Moose Mason, Betty Cooper and Jughead Jones - who have been on American news stands for years. Their Royal Highnesses' son weighs 7lbs. 3oz.
Presumably, Meghan's mom, Doria, who was also in the photograph, has known the name all along.
The newest member of the royal family looked angelic wrapped up in a white embroidered blanket with a matching white knitted hat on his head.
During a royal engagement on Tuesday, William jokingly welcomed his younger brother Harry "into the sleep deprivation society that is parenting".
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