Faber and Faber, which published James since her first book in 1962, said she died peacefully at home in Oxford, and paid tribute to "one of the world's great writers".
James sold millions of novels and won numerous international awards for crime writing, drawing on three decades of work in the civil service including in forensics work.
Fellow authors lined up to pay tribute, with Patricia Cornwell remembering her encouragement and Ian Rankin praising her "sharp intellect" and "ready wit".
Born Phyllis Dorothy James, the author only started writing in her late 30s and published her first novel, "Cover Her Face" at the age of 42.
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The book introduced Scotland Yard detective Dalgliesh, a man James said represented "all the qualities I admire in a man, sensitivity, courage and intelligence".
He went on to star in another 13 novels, including "The Murder Room", which were adapted for television.
In total James wrote more than 20 books including "The Children of Men", a dystopian novel set in England in 2021 which was made into an Oscar-nominated film.
James was a fan of detective novels as a teenager and always said she enjoyed the structure they required, dismissing critics who said they could not be serious writing.
Describing her interest in the genre, she said, "The basic moral premise, the sanctity of life, is... An attraction as is the solution of the plot at the end of the book.
"The classical detective story affirms our belief that we live in a rational and generally benevolent universe."
Although always interested in writing, her family needed the stability of a regular paycheck so she joined the civil service, a career that would end up giving her invaluable inside information for use in her books.