White, the seventh overall pick of the 2015 NFL draft, would have made $13.9 million in 2019 had Chicago exercised the option.
White, 25, has appeared in just five career regular-season games.
The West Virginia product missed his entire rookie season due to a stress fracture in his left shin that required surgery. The following year, White suffered a high-ankle sprain that eventually led to a fractured fibula in the same leg.
White then fractured his scapula in last year's season opener.
White's base salary for the upcoming season is fully guaranteed, but although Bears head coach Matt Nagy praised White's performance at the club's recently completed voluntary veteran minicamp, Chicago has not guaranteed White a prominent role on offense next year.