Introducing him to the cameras earlier in the day, Meghan said: "He has the sweetest temperament, he's really calm. He's been the dream."
As they laughed, Prince Harry said: "I don't know who he gets that from."
The announcement came after the Queen and Duke of Edinburgh met their eighth and newest great-grandchild for the first time at Windsor Castle.
By deciding to call their son Archie Harrison Mountbatten-Windsor, Harry and Meghan have chosen not to use a title for their first born.