Broncos general manager John Elway said on Saturday that Lynch's spot on the 53-man roster wasn't guaranteed.
"Vance [Joseph, head coach] and I met with Paxton this morning and informed him that it's best for everyone to make this move," Elway said in a statement Sunday. "We appreciate all of Paxton's hard work as a Bronco, and we wish him well in the future."
Lynch, who has been booed by Broncos fans during the preseason, has struggled since being selected with the 26th overall pick of the 2016 NFL Draft out of Memphis. He was unable to win the starting job from Trevor Siemian in both 2016 and 2017.
The 6-foot-7, 244-pound Lynch has posted a 1-3 mark in four career starts with four touchdowns and four interceptions. He has completed 79 of 128 passes for 792 yards in five career appearances.
The 25-year-old Hogan was acquired -- along with a sixth-round pick (No. 205 overall) in the 2018 NFL Draft -- from the Cleveland Browns in April in exchange for a sixth-round pick (No. 188).
Hogan was selected out of Stanford by the Kansas City Chiefs in the fifth round in the 2016 NFL Draft. He never played for the Chiefs and was signed by the Browns on Sept. 5, 2016.
The 6-foot-3, 218-pound Hogan appeared in eight games -- with one start -- for Cleveland, completing 60 of 101 passes for 621 yards with four touchdowns and seven interceptions. He also rushed 18 times for 176 yards with one score.
At Stanford, Hogan holds career records with 10,634 total offensive yards, 36 victories by a quarterback and 1,249 rushing yards by a quarterback.