The quarterback, who is the younger brother of Green Bay Packers QB Aaron Rodgers, was not selected during last month's draft, but attracted interest from the Jaguars and Detroit Lions as a free agent before reaching a deal with the Florida team.
The 24-year-old told Fox Sports Wisconsin: "We were focused on those two teams because of the personnel at the position, but [Jacksonville] were the best opportunity.
"They provide one of the better opportunities you can ask for as a free-agent quarterback. There's only two [quarterbacks] on the roster, and most teams have three or maybe four. It just leaves a lot of opportunity for guys like me to get my foot in the door.
"I've had to fight and claw for every position I've had. I sat on the bench as a junior in high school, I had to compete my senior year in high school to get the job, I competed again at Vanderbilt before having success. I'm not angry, it's just more motivation to want to succeed."
Rodgers won 12 of the 20 games that he started in college.