The period horror film directed by Brad Anderson, which was formerly titled 'Eliza Gravefilm' also stars Brendan Gleeson and Michael Caine, reported E! online.
Based on an Edgar Allan Poe short story, it sees a young doctor (Sturgess) taking up a post at a remote asylum.
He begins to fall for his patient (Beckinsale), but at the same time comes to realise that the original staff may have been ousted by the inmates.
Anderson's previous films include 'The Machinist' and 'Session 9'.
'Stonehearst Asylum' will be released on October 24.