Peli shot the film in his bedroom and created all the special effects using his home computer after a series of eerie sleepless nights at his house in southern California inspired the project.
It quickly become a box office sensation, returning a staggering $100 million (GBP62.5 million) on his budget of just $15,000 (GBP10,000).
Peli is handing over the project to Greutert while taking the role of producer with partner Jason Blum, according to the Hollywood Reporter. Paramount has also hired House and Law & Order: SVU writer Michael R. Perry to script the sequel.
But Peli insists Greutert is the perfect choice to take his place behind the camera. He says, "These guys get it, and the fans won’t be disappointed."
The as yet untitled follow-up is set for release on 22 October (10).