"Chose Jags because Tom Coughlin is a winner, they brought in two other big free agents and they also have been drafting well the last few years," Campbell told ESPN's Josina Anderson. "They are a young and hungry defense that I want to lead."
Campbell will sign a four-year, $60 million deal with the Jaguars that includes $30 million guaranteed, a source told ESPN's Adam Schefter.
The Jaguars are expected to sign safety Barry Church. They are also in negotiations with cornerback A.J. Bouye.
Campbell, 30, flourished in 2016 with the addition of Chandler Jones to the Cardinals' front seven, putting together one of the best all-around seasons of his career during a contract year. He had 53 tackles, 8 sacks, 3 fumble recoveries, 2 forced fumbles and 1 interception that he returned for a touchdown.
After making the Pro Bowl in consecutive seasons, Campbell, whose eight sacks tied for the second-most of his career and were the most since the nine he had in 2013, was chosen as an alternate.
Campbell's early career was spent mostly as a run-stopper, but his versatility became even more important as the 6-foot-8, 300-pounder showed he could generate inside pressure as well as push the pocket or get off blocks to help against the run.
The 30-year-old Marks had 16 sacks and five fumble recoveries in four seasons with the Jaguars. He was entering the final year of a four-year extension signed late in the 2013 season and was due to make $3.45 million in 2017.
Marks suffered a torn right ACL in the 2014 finale and missed the first five games of the 2015 season. He played in the next four games but suffered a torn right triceps muscle and missed the final seven games of the season.
The Jaguars signed free agent Malik Jackson to the richest contract in team history last March ($86.1 million over six years with $46 million guaranteed) and he became the starter at three-technique tackle. Marks played in every game as a reserve last but was unhappy with his role, telling ESPN that he didn't like being a "damn backup" but that he eventually became at peace with his new role.
The Jaguars like what they've seen from 2016 fourth-round pick Sheldon Day and also have 2015 sixth-round pick Michael Bennett on the roster. Both play the same position as Jackson and Marks, which made the older Marks expendable.
ESPN's Josh Weinfuss contributed to this report.