The 32-year-old "Swiss Army Man" star, who also wrote the script for the film with Zoe Kazan, is adapting a 1990 novel by Richard Ford, according to The Hollywood Reporter.
It centres on a teenage boy who witnesses the decay of his parents' marriage after their move to Montana.
The film's production will begin in November.
Andrew Duncan and Alex Saks of June Pictures are producing the project.
Gyllenhaal currently stars in Tom Ford's "Nocturnal Animals" while Mulligan's last big-screen appearance was in the 2015 drama "Suffragette".