The deal is for one year, sources told NFL Network's Mike Garafolo and Ian Rapoport.
Seattle lands Smith after reportedly attempting to acquire him via trade last year.
Smith spent the 2020 campaign as a member of the Dallas Cowboys after missing four seasons while serving multiple suspensions.
He started all 16 games in his return to the league last year, racking up 48 tackles, five sacks, and five tackles for loss.
Seattle has placed a priority on improving a pass rush that tallied 46 sacks but finished 31st in passing yards allowed (4,560) last season.
Smith played four seasons with the San Francisco 49ers after the club selected him with the seventh overall selection in the 2011 draft. He was named a first-team All-Pro and earned a Pro Bowl nod following the 2012 campaign.