The movie will start filming early March in New England with Kevin Walsh, Chris Moore and Matt Damon, who was originally set to star, producing it, said the Hollywood Reporter.
Lonergan wrote the script, which tells of a never-do-well plumber (Affleck) in Boston who is forced to return home to the titular town after he learns his brother passed away.
There, he finds himself thrust into the care of the man's 16-year-old son but finds himself crumbling due to a secret tragedy in his past.
Williams, who last starred in Disney's 2013 tentpole 'Oz the Great' and 'Powerful', will play Affleck's wife.