ESPN's Adam Schefter reported the deal is worth $44 million and features $26 million in guarantees.
The University of Michigan product appeared in all but two games during his four years with the Lions and has experience playing center and offensive guard.
Pro Football Focus gave him an impressive 74.1 overall player grade during the 2019 campaign.
Denver was just 7-9 last year and needs to make strides along the offensive front if it is going to compete with the reigning Super Bowl champion Kansas City Chiefs in the AFC West. According to Football Outsiders, the Broncos were a solid 10th in the league in run blocking but a mere 25th in pass protection.
The Broncos were 28th in the league in passing yards per game.
Glasgow should help Denver stabilize the offensive front as it looks to return to the playoffs for the first time since the 2015 season.