The relaxed image is less formal than the black and white portrait released to mark his last birthday.
The post was accompanied by the message: “Happy 12th Birthday to Prince George!” with a cake emoji.
Prince George is expected to celebrate his birthday privately with his family.
He will be enjoying the start of the northern hemisphere’s school summer holidays, having broken up after his penultimate year at Lambrook School just over two weeks ago.
He will spend one more year at the Berkshire prep school, which he attends with his siblings, Princess Charlotte, 10, and Prince Louis, 7, before transferring to senior school.
There has been speculation around the family’s next school choice, with Eton, the Prince’s alma mater, or Marlborough, the Princess’ former school, the likely front runners for the second in line to the throne.
Both the Prince and Princess boarded at their respective schools.
Prince George was last seen in public watching the Wimbledon men’s tennis final alongside his parents and Princess Charlotte on July 13.
The children shook hands with the players after Jannik Sinner’s victory against two-time champion, Carlos Alcaraz.
In June, the three Wales children took part in Trooping the Colour, the King’s official birthday parade, riding in the carriage procession before joining their family on the Buckingham Palace balcony to view the fly past.
