The Panthers fired coach Matt Ruhle in October and Steve Wilks was interim coach for the remainder of the season.
Carolina ended the season with a losing 7-10 record.
Reich, 61, was coach of the Indianapolis Colts for four years before he was fired nine games into this season.
He had a 40-33-1 record with the Colts where he had also served in various assistant coaching roles.
Reich won a Super Bowl ring as offensive coordinator of the Philadelphia Eagles in 2017.
As a player Reich played as mostly back-up quarterback for the Buffalo Bills from 1985 to 1994 before he moved to the expansion franchise Panthers for their first season in the league.
He later had back-up roles with the New York Jets and Detroit Lions.