The Cubs announced the move on Friday.
Dempster, who played 16 years in the majors, will serve as a special assistant to president of baseball operations Theo Epstein and general manager Jed Hoyer. He will spend time with the Cubs in spring training, visit their minor league affiliates during the season, evaluate amateur players leading up to the draft and perform professional scouting assignments.
Dempster, an All-Star with the Miami Marlins and Cubs, played in Chicago from 2004 to 2012. He also won a World Series with Boston in 2013.
He was 132-133 with 87 saves and a 4.35 ERA in 579 appearances, including 351 starts, with the Marlins, Cincinnati, Chicago, Texas and Boston.