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Sharing the photo on X, formerly Twitter, the royal couple wrote: "Wishing everyone a very merry Christmas, from our family to yours!"
The photo features Princess Charlotte sitting between her brothers Prince George and Prince Louis on a bench, with her arms slung around their shoulders.
The three beaming children are all dressed in white shirts. The photo is part of the same series that featured on the family's official Christmas card.
The photos were taken at Windsor earlier this year by Yorkshire-born photographer Josh Shinner.
The Prince and Princess joined the King and Queen at Sandringham for the traditional royal festivities, walking from the house to St Mary Magdalene Church.
For the second year in a row, the Duke of York walked to church with the family.
Andrew's alleged links to convicted sex offender Jeffrey Epstein will come under further scrutiny in the new year with the release of hundreds of files from a defamation case.
His ex-wife, Sarah, Duchess of York appeared in public at Sandringham for the first time in years, walking beside her ex-husband.
Their daughters were with their husbands, Princess Beatrice with Edoardo Mapelli Mozzi and Prince Eugenie with Jack Brooksbank.
A crowd of about a thousand gathered near the church on Christmas morning, waiting for a glimpse of the royals.
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Celebrations at Sandringham include greeting people outside the church, and a family lunch with turkey and all the trimmings.
Sandringham House has been the private home of four generations of British monarchs for more than 160 years, and now belongs to the King.
Charles's second Christmas message as monarch will be broadcast at 3pm Christmas Day.
This year it was recorded in the room that leads on to the Buckingham Palace balcony.
The room has been decorated with a living Christmas tree, which featured environmentally friendly natural ornaments and will be replanted at a later date.