The post shows the former couple as children in side by side snaps from the early 1960s.
The younger Princess of York captioned the sweet snaps: "#tbt [throwback Thursday] to my parents being adorable."
The post swiftly amassed over 24,000 likes from dedicated fans of the royal family, with a bevy of users sharing messages wishing the 59-year-old pair well.
"Precious seeing pics of them when they were young," someone wrote, while another added: "Your parents are still adorable!"
Eugenie's post prompted many to call for a romantic reunion of the Duke and Duchess of York who remain popular among the public.
"I hope they remarry!" one user said.
Another agreed: "They should get back together - they're made for each other."
Fergie was unofficially accepted back into the Windsor fold at the royal wedding of Eugenie and Jack Brooksbank last October.
Sarah, Duchess of York was photographed looking elated as she waved to the crowds outside St Georges Chapel.
Queen Elizabeth is known to have retained a soft spot for her fiery daughter-in-law despite divorcing her second son.