Gavin O'Connor will direct the film, which centres around a mild mannered accountant (Affleck) who moonlights as an assassin, according to Variety.
Kendrick and Simmons, 59, both starred in 2009 film 'Up in the Air'.
The 29-year-old actress will next be seen in Disney's adaptation of the musical 'Into the Woods', and will return for 'Pitch Perfect 2'.
Simmons stars alongside Miles Teller in the acclaimed new drama 'Whiplash'.
'The Accountant' will go on floors in January next year.