A statement from her publisher, Harper Collins, said she "passed away peacefully at her London home in the early hours of this morning".
Her best-known works include The Golden Notebook, Memoirs of a Survivor and The Summer Before the Dark.
She became the oldest winner of the Nobel Prize for Literature when in 2007 she won the award for her life's work aged 88.
Jonathan Clowes, her long-time friend and agent, said she was "a wonderful writer with a fascinating and original mind".
"It was a privilege to work for her and we shall miss her immensely."
"Doris Lessing was a one of the great writers of our age," said Charlie Redmayne, CEO of Harper Collins UK.
She was only the 11th woman to receive the Nobel Prize for Literature"She was a compelling storyteller with a fierce intellect and a warm heart who was not afraid to fight for what she believed in."
The author Fay Weldon praised Lessing for "her concern for humanity, her sense of the sweep of history and her ability to place human beings in it".
"She was just the most remarkable writer and we won't see her like again," she added.
Lessing is survived by her daughter Jean and granddaughters Anna and Susannah.
Born in what is now Iran, she moved to Southern Rhodesia - now Zimbabwe - as a child before settling in England in 1949.
Her debut novel The Grass is Singing was published in 1950 and she made her breakthrough with The Golden Notebook in 1962.
On winning the Nobel Prize, the Swedish Academy described Lessing as an "epicist of the female experience, who with scepticism, fire and visionary power has subjected a divided civilisation to scrutiny".
After learning she had won the award, she said she was "very glad" but recalled that in the 1960s she had been told the Nobel Prize committee did not like her and she would never win one.
Fay Weldon: "I will remember Doris Lessing as a great person and a great writer"
"So now they've decided they're going to give it to me. So why? I mean, why do they like me any better now than they did then?" she said.
The Swedish Academy said the Golden Notebook was seen as "a pioneering work" that "belongs to the handful of books that informed the 20th Century view of the male-female relationship".
As an author, though, Lessing distanced herself from the feminist movement.
The content of her other novels ranged from semi-autobiographical African experiences to social and political struggle, psychological thrillers and science fiction.
She had two children with her first husband, Frank Wisdom, whom she married in 1939. But she left the family home and the couple divorced in 1943.
She then married and had a son with the German communist Gottfried Lessing in 1945.
They divorced in 1949 and she moved to England with her son Peter.
Tributes have been paid to Lessing by her fellow authors, with Professor Lisa Jardine remembering her as "one of our very greatest writers".