Her agent Simon Beresford said she "died at home with her family who have asked for privacy at this hard time".
Simon Beresford, her agent, said in a statement that she had died "peacefully" early on Thursday morning at home with her family, who had asked for privacy.
Rigg had been diagnosed with cancer in March.
Rigg is survived by her daughter, son-in-law Guy Garvey - lead singer of the band Elbow - and a grandson.
Rigg also starred in the West End production of Stephen Sondheim's musical Follies in 1987, and, from 1992, played Medea at the Almeida, in the West End and on Broadway (winning a Tony Award for her work).
She also played the Duchess of Buccleuch in ITV royal drama Victoria, the young queen's mistress of the robes, who is "renowned for speaking her mind".
Rigg, who grew up in India after her father accepted a job there, trained at the Royal Academy of Dramatic Art and made her acting debut in "The Caucasian Chalk Circle" at the 1957 York Festival.
1981: Lady Holiday, played by Diana Rigg, gives instructions to her secretary, Miss Piggy, in Jim Henson's "The Great Muppet Caper".
She then hosted Masterpiece Mystery from 1989 through 2004, appeared on Dr. Who in 2013, and then picked up the role of the sassy yet wise Olenna Tyrell later that year.
"She was ahead of her time", Rigg once said of her beloved Avengers character.
Patrick Macnee passed away back in 2015, and now he's joined by his partner in espionage as Diana Rigg has passed away at age 82.
Rigg died on 10 September 2020 with her family.
She was most recently seen on British television screens in "All Creatures Great and Small", a series about the life of a vet.
Diana's friend and talent agent Lionel Larner told Variety, "She was a handsome kind and generous human being that enhanced the lives of all that knew her as well as a great actress". From three slightly hysterical months at the Old Vic in All About Mother to writing The Crimson Horror for Diana and her wonderful daughter Rachael.
Rigg amassed an extensive acting resume over her almost 60-year-long career.
In a nude scene she played in Abelard And Heloise, she was described by one critic as being "built like a brick mausoleum with insufficient flying buttresses".
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