His addition gives the Cardinals a replacement for Mike Iupati, who is a free agent after finishing the 2018 season on injured reserve.
Sweezy, who turns 30 in April, has played right and left guard during his seven-year NFL career.
The NFL Network first reported Sweezy's deal with Arizona, which cannot become official until the start of the new league year Wednesday.
Sweezy made 15 starts for the Seahawks in 2018 after re-joining the team on a one-year deal that paid him around $1.8 million factoring in roster and playing-time bonuses. Speaking at the NFL scouting combine last month, Seahawks coach Pete Carroll said it was nice to finally be "established" up front, referring to continuity that Seattle's offensive line had lacked in recent seasons.
But Sweezy's departure means the Seahawks will have to replace at least one starting guard and possibly two with D.J. Fluker unsigned after playing on a one-year deal.
Sweezy spent his first four seasons with the Seahawks after they drafted him in the seventh round in 2012 out of North Carolina State, where he played defensive tackle. He left Seattle for a five-year, $32.5 million deal with the Tampa Bay Buccaneers in 2016. He missed that season while recovering from back surgery and was released last offseason after starting 14 games in 2017.