Lessing, who will be 88 on October 22, is only the 11th woman to have won the prize since it was first awarded in 1901.
The Swedish Academy described her as "that epicist of the female experience who with scepticism, fire and visionary power has subjected a divided civilisation to scrutiny."
A spokeswoman for Lessing's literary agency Jonathan Clowes told AFP on hearing the news: "We are absolutely delighted because it is so well deserved. She doesn't know yet ... She's out shopping and we are trying to get in touch with her before she discovers it in the news."
Lessing, whose work has covered a multitude of topics, has over the years been mentioned as a possible Nobel laureate but she was not seen as among the frontrunners this year.
Although "The Golden Notebook", her best known work, established her as a feminist icon back in 1962, she has consistently refused the label and says her writing does not play a directly political role.
Nonetheless, for the Nobel jury, "the burgeoning feminist movement saw it as a pioneering work and it belongs to the handful of books that informed the 20th century view of the male-female relationship."
Born Doris May Taylor in Khermanshah, in what is now Iran, on October 22, 1919, Lessing spent her formative years on a farm in Southern Rhodesia, what is now Zimbabwe, where her British parents moved in 1927.