The official Twitter account of the Prince of Wales and the Duchess of Cornwall posted an image of Charles and Anne as small children alongside a birthday message.
The black and white photograph, from 1951, shows the pair in prams in the garden of Clarence House in London.
The message said: “Wishing The Princess Royal a very Happy Birthday today.
“In this photo from 1951, The Prince of Wales squeezes his younger sister’s hand while sitting in their prams in the Clarence House garden.”
The Queen’s official Twitter account posted four photos of Anne, including one of her with her mother.
An accompanying message said: “Wishing HRH The Princess Royal a happy birthday today.”
Anne was born at Clarence House on August 15 1950 as third in line to the throne but was leapfrogged by her younger brothers Andrew and Edward when they were born.
The princess is now 16th in line to the throne.
A skilled horsewoman, she competed at the 1976 Montreal Olympics as a three-day eventer in the British equestrian team, riding the Queen’s horse Goodwill.
Last month, Anne recalled the thrill of competing in the Games as she sent a good luck message to Team GB ahead of Tokyo 2020.
In a video message, the princess, who is president of the British Olympic Association, said: “Although I am sad not to be there in person, I and the whole nation will be cheering for you and proudly supporting you from home.
“I do remember from my own Olympic journey the anticipation and excitement of stepping onto the Olympic stage.
“But also the single-minded focus on what you need to do.
“I know that you have all worked incredibly hard for this moment during the most challenging of times, and I hope you will find the Team GB environment a support and an inspiration for you.”
The Princess Royal regularly tops the list of royals with the most engagements and is widely known as one of the hardest-working senior members of the family.
She married her first husband, fellow horseman Captain Mark Phillips, in 1973.
The couple survived a kidnapping attempt the following year and had two children, Peter, born in 1977, and, four years later, Zara, herself a silver medal-winning Olympic horsewoman.
Anne married her second husband, Vice Admiral Sir Tim Laurence, in a low-key ceremony in 1992, after her marriage to Phillips ended in divorce after 19 years.