She had been diagnosed with cancer earlier this year and died peacefully at home, her daughter said.
A statement from her agent Simon Beresford said: “It is with tremendous sadness that we announce that Dame Diana Rigg died peacefully early this morning.
“She was at home with her family who have asked for privacy at this difficult time.
“Dame Diana was an icon of theatre, film, and television. She was the recipient of Bafta, Emmy, Tony and Evening Standard Awards for her work on stage and screen.
“Dame Diana was a much-loved and admired member of her profession, a force of nature who loved her work and her fellow actors. She will be greatly missed.”
Her daughter Rachael Stirling said: “My Beloved Ma died peacefully in her sleep early this morning, at home, surrounded by family.
“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.”
Dame Diana was best known for her roles as Emma Peel in the TV series The Avengers, and more recently for playing Olenna Tyrell in Game of Thrones.
She also played Countess Teresa di Vicenzo, James Bond’s wife, in On Her Majesty’s Secret Service and was a highly acclaimed theatre actress.
She was created a dame in 1994 for services to drama.
Playwright Sir David Hare said: “Diana Rigg had a dazzling change of direction in middle age as a great classical actor.
“When Emma Peel played Euripides’ Medea, Albee’s Martha and Brecht’s Mother Courage she swept all before her.”
Playwright Sir Tom Stoppard added: “For half her life Diana was the most beautiful woman in the room, but she was what used to be called a trooper.
“She went to work with her sleeves rolled up and a smile for everyone. Her talent was luminous.”
Theatre director Jonathan Kent said: “Diana Rigg’s combination of force of personality, beauty, courage and sheer emotional power, made her a great classical actress – one of an astonishing generation of British stage performers.
“I was so fortunate to direct her in a series of great classical roles – Medea, Phedre – in Ted Hughes’ version, specially written for her – Mother Courage and Dryden’s Cleopatra. Her dazzling wit and that inimitable voice made her an unforgettable leading figure in British theatre.”
