The 24-year-old has swapped west London for the City Ground, where he had a spell on loan last season, and agreed a four-year deal.
Camp, a former England Under-21 international, made 76 appearances for Rangers but lost his first-team place to Czech veteran Radek Cerny last term.
He becomes Forest's fourth signing of the close-season, joining David McGoldrick, Dele Adebola and Paul Anderson at the club.
Source: Team_Talk