Helfrich spent 2017 out of football after Oregon fired him at the conclusion of the 2016 campaign.
He took over as Oregon's head coach in 2013 following the departure of Chip Kelly, and posted a 37-16 record in four seasons.
That included a 13-2 record in 2014, which ended with a 42-20 loss to Ohio State in the inaugural College Football Playoff National Championship Game.
Oregon struggled to a 4-8 mark in 2016, although it still ranked 27th in the nation in scoring.
In the three seasons leading up to that, the Ducks were fourth, fourth and fifth in points scored with Helfrich at the helm.
Prior to becoming Oregon's head coach, Helfrich was the offensive coordinator and quarterbacks coach for the Ducks from 2009 through 2012.
He also had stints as an assistant at Boise State, Arizona State and Colorado. The Bears job will be his first in in the NFL.
Chicago ranked in the top 10 defensively this season, but was 30th in total offense and 29th in points per game.
The Bears figure to open things up with Helfrich in charge of the offense, and he should aid in the development of young quarterback Mitchell Trubisky as well since the former Ducks coach was key to Marcus Mariota's success at Oregon.