The novelist, playwright and screenwriter's body of work includes more than 30 novels, as well as short stories and plays written for television, radio and the stage.
A family statement said: "It is with great sadness that we announce the death of Fay Weldon (CBE), author, essayist and playwright. She died peacefully this morning January 4, 2023."
The writer previously told her readers in a statement posted on her website that she had been admitted to hospital with a broken bone in her back and then with a stroke.
Born in September 1931, she was brought up in New Zealand and returned to the UK as a child.
She went on to read economics and psychology at the University of St Andrews in Scotland and later received an honorary doctorate from the institution in 1990.
Weldon worked briefly for the Foreign Office in London and as a journalist before moving to work as an advertising copywriter.
She left this career to focus on her writing and published her first novel, The Fat Woman's Joke, in 1967.
Alongside her prolific novel career, she also wrote children's books, non-fiction books and newspaper articles.
She was also one of the writers on the popular drama series Upstairs, Downstairs which ran from 1971 to 1975, receiving an award from the Writers Guild of America for the show's first episode.
Much of her fiction explores issues surrounding women's relationships with men, children, parents and each other, including the novels Down Among The Women (1971) and Female Friends (1975).
Her 1978 novel Praxis was shortlisted for the Booker Prize for Fiction and she later chaired the judges' panel for the prestigious award in 1983.
She published a memoir called Auto Da Fay in 2002 when she was 70.
Weldon was also a professor of creative writing at Bath Spa University, retiring in 2021.
After spending nine years teaching at the institution she was awarded Emeritus Professor status in recognition of her dedication to the university.
She was made a CBE for her services to literature in the New Year Honours list in 2001.