The deal has been struck through Lawrence's literary agent Pollinger.
Sony has commissioned Oscar nominated American screenwriter David Magee, who scripted the film adaptation of Yann Martel's Life of Pi, to produce the script. This will be the fifth screen incarnation of the novel, but the first to make it to Hollywood.
Lawrence's controversial novel tells the story of an affair between a young married aristocratic woman and her husband's gamekeeper. It was first printed privately in Italy in 1928, but was banned or censored in several countries due to its explicit language and sexual content.
When Penguin Books published an uncensored version openly in Britain in 1960, it faced an obscenity trial for doing so, though it was found not guilty after evidence was heard from academic critics including E M Forster.