Rigg won numerous Emmy, Tony and Bafta awards during her long and prestigious career, equally at home in classical theatre roles as those in popular TV shows.
"My Beloved Ma died peacefully in her sleep early this morning, at home, surrounded by family," her actress daughter Rachael Stirling said in a statement.
"She died of cancer diagnosed in March, and 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, born in Doncaster in northern England, moved with her family to India before going to school in England.
She studied at the Royal Academy of Dramatic Art before making her debut at the Royal Shakespeare Company in 1959.
She went on to star in the James Bond film On Her Majesty's Secret Service in which her character marries the British spy.
A return to the theatre resulted in a string of hits in the 1970s and 80s, and she was acclaimed for her role as Medea in the early 1990s for which she won a Tony.
Recently, she is best known for playing Olenna Tyrell in Game of Thrones.
Rigg's Game of Thrones co-star Peter Dinklage posted a tribute to Twitter.
"For half her life Diana was the most beautiful woman in the room, but she was what used to be called a Trouper. She went to work with her sleeves rolled up and a smile for everyone.
Her talent was luminous," British playwright Tom Stoppard said in a statement.
