Bell, 28, and fellow Bengals safety Jessie Bates are both unrestricted free agents.
Tuttle agreed to a three-year contract worth $19.5 million, ESPN and NFL Network reported, and helps the Panthers in their transition to a 3-4 defense.
Tuttle gets $13 million guaranteed at signing, per the reports.
Both deals can become official on Wednesday, the first day of the new league year.
Bell was a second-round pick in 2016 by the New Orleans Saints. He had a career-high four interceptions last season with the Bengals.
Bengals defensive coordinator Lou Anarumo said losing Bell and Bates would be a "dark day" in Cincinnati because of all the contributions they make to the team that go unseen.