Helfrich, a 44-year-old Oregon native, was the Ducks' offensive coordinator for four seasons before he replaced Chip Kelly as head coach in 2013. He went 37-16 in four seasons at Oregon but was fired after his team finished 4-8 in 2016.
Helfrich, who also previously served as the offensive coordinator at Colorado and passing-game coordinator at Arizona State, spent last season as a television analyst for Fox Sports. He has never coached in the NFL.
ESPN first reported Helfrich's hiring Thursday morning.
New Bears coach Matt Nagy, who was hired earlier this week, most recently worked as offensive coordinator of the Kansas City Chiefs. Nagy said in his introductory press conference that he will call the plays for the Bears in 2018.