Adams, 35, went from being a June signing in 2014 by the Indianapolis Colts to being selected to back-to-back Pro Bowls after the 2014 and 2015 seasons by tying for the league lead with seven takeaways in 2014 and posting five interceptions in 2015.
In a team release announcing the signing, Adams said his decision was motivated by his chase for a Super Bowl.
"When you get older, you realize your time is running out. It's time to get that ring," Adams said. "I just want to win, want to turn over a new leaf and Carolina is the spot."
Adams was reminded numerous times about his age after being introduced to media in Charlotte.
"You guys pay attention to that," he said. "So what I have to say to that is stop looking at my bio and watch the film. That's what I have to say to everybody. My body of work and what I've [done] speaks for itself.
"If you see my film and watch my film, you wouldn't know how old I am."
Adams said the same thing when told the Panthers have reached an agreement with 37-year-old defensive end Julius Peppers.
"Stop looking at Julius Peppers' bio, too," Adams said. "Don't look at his, because his body of work is phenomenal. He's ballin'. At the end of the day you can say age all you want. But if you look at the productivity ... just look at that for a second.
"Because when you say to us the age and we start talking about that, it discourages GMs. They get scared upstairs. So y'all got to keep that to a minimal."
Adams said he came to Carolina to compete for a starting job, not to be given one.
"They're not giving me anything," he said. "They're not giving me the job, 'cause I don't want that. I want to compete."
Colts coach Chuck Pagano often referred to Adams, who was the anchor of the defense and led the team in tackles (79) last season, as an extra coach because he knew all of the assignments of his 10 defensive teammates.
Durability is a strong suit of the 13-year veteran. Adams has only missed five games during the past eight seasons.
ESPN's David Newton and Mike Wells and The Associated Press contributed to this report.