Jacksonville also released safety Tashaun Gipson, right tackle Jeremy Parnell and long snapper Carson Tinker. The Jaguars announced the roster moves Friday.
Jackson, 29, started 10 games and appeared in 16 contests in 2018. The 2017 Pro Bowl selection played his first four seasons for the Denver Broncos after being picked in the fifth round of the 2012 NFL Draft.
The 6-foot-5, 290-pound defensive lineman won a Super Bowl in 2016 with the Broncos, before signing a six-year, $90 million contract with the Jaguars a month later.
Hyde, 28, joined the Jaguars in a trade from the Cleveland Browns in October. The five-year veteran had 571 yards and five touchdowns on 172 carries in 2018. Hyde had 189 yards on 58 carries in eight games for the Jaguars following the trade.
The Ohio State product played his first four seasons for the San Francisco 49ers after being selected in the second round of the 2014 NFL Draft. Hyde had a career-best 1,288 yards from scrimmage in 2017 for San Francisco.
Jacksonville cleared $11 million in salary cap space by releasing Jackson. Hyde's release clears $4.7 million off of the cap for 2019. The Gipson move clears $7.45 million off of the cap. The moves save the Jaguars $23.15 million in total salary cap space.