Screenwriter Bill Wheeler will handle the film adaptation and also co-produce, Daily Variety reported Tuesday.
Greenfield's book follows the rise of Leary from a Harvard professor to prominent voice of the 1960s anti-establishment movement.
Greenfield -- a former associate editor of Rolling Stone's British operation -- also wrote "S.T.P.: A Journey Through America With the Rolling Stones," "Bill Graham Presents: My Life Inside Rock and Out" and "Dark Star: An Oral Biography of Jerry Garcia."
Harcourt Books is publishing the biography June 6.