In a message, the couple said: «Thank you for all of the love and support from so many of you around the world. Each of you made this day even more meaningful.»
The pictures feature a series of black and white images by Chris Allerton, including one that appears to be Harry thumbing a lift and another where Meghan is holding hands with her mother, Doria Ragland.
The famous picture of the couple sharing a kiss on the steps, by Press Association photographer Danny Lawson, is also among the snaps shared.
The birth of Harry and Meghan’s son came less than a year after the royal nuptials attended by A-list stars like Oprah Winfrey, George and Amal Clooney, and the British monarchy led by the Queen and the Duke of Edinburgh.
Harry, 34, and Meghan, 37, got engaged following a whirlwind 16-month romance after going on a blind date in London.
Archie’s birth was registered on Friday, revealing the couple had their baby at London’s Portland Hospital, a private hospital favoured by celebrities.
The baby, who is the seventh in line to the throne and an eighth great-grandchild for the Queen and Prince Philip, arrived at 5.26am on May 6, weighing 3.2 kilograms.
The birth certificate lists Harry’s occupation as «Prince of the United Kingdom» and Meghan as «Princess».
Archie, who was not given a courtesy title, met his uncle and aunt, the Duke and Duchess of Cambridge, for the first time on Tuesday, having already spent time with his royal great-grandparents, the Queen and Prince Philip.