A statement from her agent reads: "She died peacefully early this morning [September 10, 2020]. She was at home with her family who have asked for privacy at this difficult time."
Her daughter, the actor Rachael Stirling, said Rigg had been diagnosed with cancer in March. She said she "spent her last months joyfully reflecting on her extraordinary life, full of love, laughter, and a deep pride in her profession. I will miss her beyond words."
Rigg first came to national attention playing Emma Peel in the TV series The Avengers through 1965 to 1968. From there, she landed the role of Tracy Bond in 1969's On Her Majesty's Secret Service opposite George Lazenby's James Bond.
An attempt to break into America was initially less successful, as the sitcom Diana, in which she played the title character, was cancelled after 15 episodes. Throughout that period, she continued to work on a steady stream of movies, including an adaptation of Witness for the Prosecution and a leading role in Jim Henson's The Great Muppet Caper.
Rigg later found fame again playing Olenna Tyrell in the series Game of Thrones. She also appeared in BBC's Detectorists and ITV's Victoria, as well as an appearance in Andy Serkis' Breathe. Her last role will be opposite Anya Taylor-Joy in Edgar Wright's upcoming movie Last Night in Soho.
On twitter, Wright paid tribute to the actor: "What to say about Diana Rigg? I could talk about her incredible career, but for now I'll just say as a lifelong fan, it was beyond a thrill to work with her on her final film. She exceeded all my highest expectations, so blazingly talented, fiery and funny. Miss you already Dame D."