According to her sons Samuel and Joseph, she was watching the classic British comedy “the day before she died”.
Their statement said: “Our darling mother Prunella Scales died peacefully at home in London yesterday. She was 93.
“Although dementia forced her retirement from a remarkable acting career of nearly 70 years, she continued to live at home.
“We would like to thank all those who gave Pru such wonderful care at the end of her life: her last days were comfortable, contented and surrounded by love.”
Paying tribute John Cleese described Prunella Scales as “a really wonderful comic actress,” adding: “Scene after scene she was absolutely perfect.”
Ms Scales is survived by two sons and one stepdaughter, seven grandchildren and four great-grandchildren.
She was diagnosed with vascular dementia in 2013 and her death comes 50 years on from when Fawlty Towers first appeared on screens.
Before taking on the role of Sybil, Scales teamed up with Ronnie Barker in the BBC series Seven Of One.
She would go on to portray Queen Elizabeth II in Alan Bennett’s 1991 televised play A Question of Attribution, a role for which she received a Bafta nomination.
Her husband, fellow actor Timothy West, died in November last year.
Mr West starred in TV shows such as comedy drama Brass, sitcom Not Going Out and soaps Coronation Street and EastEnders.