The deal is worth more than $22 million and could reach $24 million following incentives, per NFL Network's Mike Silver.
Reid, 27, appeared in 13 games (all starts) for Carolina last season after signing with the club on as a free agent on Sept. 28. He recorded 71 tackles, defended five passes and recorded one interception.
Reid, a 2013 first-round pick of the 49ers, began joining former teammate Colin Kaepernick in protesting police brutality and racial inequality by kneeling during the national anthem in 2016.
Reid went unsigned throughout the 2018 offseason, making just one free-agent visit with the Bengals. The NFLPA later filed a grievance against the NFL on his behalf in a lawsuit alleging that team owners and the league colluded to prevent his employment because of his protests under the influence of President Donald Trump.