The deal is understood be short term and until the end of this season. City are currently 16th in the Championship table and 12 points adrift of the play-off positions.
Hodgson briefly managed Bristol City in 1982 near the start of a managerial career that has spanned more than 50 years. His first job was with Swedish club Halmstad in 1976.
He has also managed Malmo, Blackburn Rovers, Inter Milan, Fulham, Liverpool and Watford, among others.
Hodgson managed the England national team from May 2012 to June 2016, departing after a humiliating defeat by Iceland at Euro 2016.