King Charles III and Queen Camilla have led tributes to famed playwright Sir Tom Stoppard, who died aged 88, hailing him as "one of our greatest writers".

"A dear friend who wore his genius lightly, he could, and did, turn his pen to any subject, challenging, moving and inspiring his audiences, borne from his own personal history," they said.

Sir Tom, who won an Oscar and a Golden Globe for the screenplay for Shakespeare In Love, "died peacefully at home in Dorset, surrounded by his family", his agents said on Saturday.

Tributes have poured in from around the world for the playwright who captivated audiences for more than six decades with work that explored philosophical and political themes.

The King and Queen added they were "deeply saddened" by Sir Tom's death and sent their condolences to his family.