The 28-year old Lutui originally agreed to a two-year contract with the Bengals on Friday but signed a one-year deal with Arizona on Sunday after failing the physical.
Lutui, listed at 6-foot-4 and 338 pounds, was a second-round pick of Arizona in 2006 out of USC.
According to The Arizona Republic, Lutui still has to pass a physical with the Cardinals before his latest deal becomes official.
Arizona has already signed free agent guard Floyd Womack, an 11-year NFL veteran who played in 16 games for Cleveland last season. Womack is the second new guard on the line. Daryn Colledge, a starter on the Green Bay Packers' Super Bowl championship team, signed a free-agent deal with Arizona, taking the spot left open by the retirement of Alan Faneca.
The team kept some continuity on the interior line by re-signing center Lyle Sendlein.
Information from ESPN NFL Insider Adam Schefter and The Associated Press contributed to this report.