The Sony Pictures production is the true story of an army commander - to be played by Pitt - and his crew members who go behind enemy lines in their tank just as Nazi Germany collapses at the end of the war in 1945.
Lerman will play young and inexperienced crew member Norman Ellison, who is thrown into the role of being a tank gunner.
Writer-and-director Ayer is helming the picture based on his own script.
Lerman will next be seen in young adult action adventure flick, 'Percy Jackson: Sea of Monsters', a sequel to 2009's 'Percy Jackson and the Lightning Thief'.
Meanwhile, Pitt will next be seen in another war film - the postapocalyptic action movie 'World War Z', which is in cinemas this summer.
'The Fury' - which has a rumoured budget of $80 million - is expected to begin filming later this year.