He was in residence at the estate when his mother, Queen Elizabeth II, became gravely ill shortly before her death in September 2022.
The content of King Charles’ letter will remain unknown until it is excavated in a century’s time.
Kristina Murrin, the charity’s chief executive, said: “We are so proud of what The King’s Foundation has achieved over the past 35 years.
“I hope those uncovering the time capsule in 2125 will recognise the positive impact both the King and his foundation have had on the world and its communities.”
King Charles also hosted an audience with Julius Maada Bio, president of Sierra Leone, at the property.
The King was joined by television presenter and charity ambassador Alan Titchmarsh at the event.
Stewart, 80, and Lancaster, also known as Lady Stewart, are among a number of well-known ambassadors of the charity.
Former England football captain David Beckham and actor Sienna Miller have also served in the role.
Stewart said: “We are so pleased to be coming on board as ambassadors for The King’s Foundation and look forward to lending our support to this worthwhile cause, particularly during such a significant year for the charity.”