HanWay films is handling internationals sales.
John Maybury is directing the project, which is now searching for a new Cathy after Natalie Portman pulled out last week.
Fassbender previously appeared in 300 and also in Joel Schumacher's forthcoming Creek.
Ecosse's Robert Bernstein, who is producing, said: 'Heathcliff is one of the most powerful and iconic romantic roles, Fassbender is now the most exciting British contemporary actor'.
'Heathcliff is the blueprint for all modern romantic leading men - Fassbender has a touch of genious about him - he'll be a revelation - brooding, wild and dangerous - he could be a Brando for Britain', added HanWay's Tim Haslam.