The one minute-long video uses images from their personal wedding photographer Chris Allerton, giving fans a glimpse into the previously unseen moments from the day.
It includes pictures of the couple signing the register at St George's Chapel, which was not captured by television cameras.
Other pictures show Prince Harry and his best man Prince William walking down the stairs to begin their day, and Meghan holding hands with her mother, Doria.
A message published with the picture reads: "Happy one year anniversary to Their Royal Highnesses, The Duke and Duchess of Sussex!
"Today marks the one year anniversary of the wedding of The Duke and Duchess of Sussex.
"Their Royal Highnesses exchanged vows at St George’s Chapel within the grounds of Windsor Castle on May 19th, 2018.
"The selected song 'This Little Light of Mine' was chosen by the couple for their recessional.
"We hope you enjoy reliving this moment, and seeing some behind the scenes photos from this special day.
"A message from The Duke & Duchess: '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 Duke and Duchess of Sussex celebrate their first wedding anniversary on Sunday as a family of three following the arrival of baby Archie.
Their son's birth came less than a year after the royal nuptials at Windsor Castle, a wedding attended by A-list stars like Oprah Winfrey and George and Amal Clooney as well as the Royal Family led by the Queen and the Duke of Edinburgh.
Harry, 34, and Meghan, 37, announced their engagement following a whirlwind 16-month romance after going on a blind date in London.
Their wedding was seen around the world, with fans travelling to the UK to share their good wishes with the new American member of the Royal Family.
The following year saw the Duchess launch the Grenfell cookbook, a major Commonwealth tour to Australia, Fiji, Tonga and New Zealand, and move to Frogmore Cottage and a baby.
A first wedding anniversary is traditionally celebrated with paper gifts, with couples sometimes exchanging presents featuring a paper ticket.
Meghan's mother Doria Ragland - now a grandmother for the first time - is thought to be staying with the couple and could perform babysitting duties if the duke and duchess choose to have a romantic dinner to mark their anniversary.
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 Philip, arrived at 5.26am on May 6, weighing 7lb 3oz.