The 81-year-old author was chosen by a panel which included Poet Laureate Andrew Motion, who was chair, as well as actor Simon Callow, Claire Armitstead, literary editor of The Guardian, and biographer Michael Holroyd.
The prize is awarded every two years to a writer in recognition of a lifetime's achievement in literature.
Ms Lessing was presented with the prize by Culture Secretary Chris Smith at a ceremony at Coutts Bank in London.
The 81-year-old author was chosen by a panel which included Poet Laureate Andrew Motion, who was chair, as well as actor Simon Callow, Claire Armitstead, literary editor of The Guardian, and biographer Michael Holroyd.
A quarter of the prize money is given to enable the winner to support a young writer or literature organisation.
Miss Lessing has requested that the money is given to The Art of Regeneration, a programme led by the National Theatre which works with young people in and around Deptford, south-east London.
"I have been part of an astonishing period in this country's literature. I am proud to have been part of it.
"And proud that this prize you have given me acknowledges that I have been part of it."
The David Cohen prize was set up in 1991 and previous winners include V S Naipaul, Harold Pinter, Muriel Spark and William Trevor.
'Literary landscape'
Gerry Robinson, chairman of the Arts Council of England, said: "We recognise individual achievement; we acknowledge, as it were, an accumulation of excellence, a body of work that has, in its unique and determined way, shaped the literary landscape."
Ms Lessing has been one of the towering figures in British literature for the last 50 years and, along with Iris Murdoch, is considered to be among the greatest female writers of the 20th century.
She has been awarded numerous prizes including the Somerset Maugham Award in 1956 and the WH Smith Award in 1986 and has been shortlisted three times for the Booker prize.
A prolific writer, she has written at the rate of a book a year over the last half-century and still writes for three or four hours a day.