The deal follows on from the announcement earlier this week that Grindstone had also bought ghostly thriller Room 205 from Nordisk.
Grindstone will be working in partnership with producer Ghost House Pictures on the release. Ghost House Pictures' recent releases include 30 Days of Night, The Messengers and Boogeyman.
The Substitute, from acclaimed Ole Bornedal (Nightwatch), follows a terrified 6th grade class as they race to reveal to their parents that their new substitute teacher is an evil alien being.
The sale was brokered by Tine Klint for Nordisk Film International Sales and Stan Wertlieb for Grindstone.
The Substitute is produced by Michael Obel of Thura fiction k/s and was Denmark's biggest local hit in the summer with almost 200,000 admissions.