A spokeswoman for her husband, Maurice, Lord Saatchi, 64, said Hart died in London on Thursday after battling cancer.
She was in her late 60s, but was always “coy and secretive” about her exact age, her literary agent, Ed Victor, said.
Hart’s first novel, Damage, about a politician who has an affair with his son’s lover, was a best-seller and was made into a film staring Jeremy Irons and Juliette Binoche.
Hart, who was born in Ireland, was due to present a series of poetry readings at the Donmar Warehouse in London’s Covent Garden this week.
One of her last acts was to release a statement to the Evening Standard in which she said her life would have been “less comprehensible, less bearable and infinitely less enjoyable” without reading and poetry.