Uploading family photos on their social media accounts, Prince William and Kate wrote "Wishing His Majesty The King a very happy 75th birthday!" alongside a cake emoji.
One photo showed William and his dad on a previous ski holiday, while another was a solo portrait of His Majesty. A third showed the Wales family with the King and Queen, posing on the balcony of Buckingham Palace at Trooping the Colour this year.
It comes after the King joined fellow 75-year-olds for a special party at his Gloucestershire home, Highgrove, on Monday.
The afternoon tea, which featured dancing with live music from a local rock choir, also marked the 75th anniversaries of the NHS and the Windrush generation in 2023.
On Tuesday, the King and Queen will officially launch the Coronation Food Project, which aims to bridge the gap between food waste and food needs across all four nations of the United Kingdom, helping people and helping the planet.
Later, Charles will also host a reception at Buckingham Palace for 400 nurses and midwives, as part of this year's NHS 75 celebrations.
William and Kate, who joined the King and Queen for Remembrance events last weekend, are also expected to be among the guests at Charles's private family party on Tuesday evening.
Close family and friends will reportedly gather at the King's London home, Clarence House.
The Duke and Duchess of Sussex, who reside in Montecito, California, are not expected to attend.
A spokesperson for Prince Harry and Meghan said: "In response to UK media headlines, there has been no contact regarding an invitation to His Majesty’s upcoming birthday."
Harry has spoken of his complicated relationship with his father Charles, and older brother William in his and Meghan's Netflix docuseries and his tell-all memoir, Spare.
For the then Prince's 70th birthday in 2018, Queen Elizabeth II hosted a reception at Buckingham Palace, with guests including the Waleses and the Sussexes, spotted making glamorous arrivals at the time.
The palace also released family portraits of Charles and Camilla, with William and Kate and their three children, and Harry and Meghan.
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