The pair will play actors Janet Leigh and Anthony Perkins in Sacha Gervasi's biopic charting the making of the legendary film, reports Variety.
The movie focuses on Hitchcock's struggle to fund his now classic 1960 horror film, for which he received disapproval and ridicule at the time.
Anthony Hopkins will play the director, with Helen Mirren cast as his wife Alma Reville.
The adaptation of Stephen Rebello's non-fiction tale of the making of the classic movie has been in the works for several years. It was initially being developed at Paramount by Glee co-creator Ryan Murphy before passing to Gervasi.
Johansson recently starred in Cameron Crowe's We Bought a Zoo and will feature in Joss Whedon's forthcoming Avengers movie.
D'Arcy starred in Madonna's W.E. as King Edward VIII.