Hodgson previously managed Bristol in 1982, his first coaching assignment at an English club.
The 78-year-old, who was last in charge of Crystal Palace, led Inter Milan to the UEFA Cup final in 1996-97, and took Fulham to the Europa League final in 2009-10.
Bristol sit 12 points above the relegation zone with seven matches to go in the Championship, but have not won a game since last month, as their FA Cup campaign ended in a loss to League One side Port Vale.
"Roy's appointment is about more than the results of the next seven games. Over the remainder of the season, he will help us set the standards and values at the club that we will need to be successful going forwards," Bristol CEO Charlie Boss said in a statement.
Bristol next face Charlton Athletic on April 3rd.