The Cardinals also made a key addition to their special teams, agreeing to terms with wide receiver/kick returner Josh Cribbs, according to reports.
Cardinals coach Bruce Arians was at one time Mendenhall's offensive coordinator with the Steelers.
Mendenhall had led the Steelers in rushing for three straight seasons before a disappointing 2012 season marred by injuries and a one-game suspension for conduct detrimental to the team.
He was suspended for a game in December for not attending a loss to the Chargers after he found out he wouldn't dress for the game. He also was inactive for two games after fumbling twice on four carries in a loss to the Browns.
Mendenhall also was slowed by injuries. He tore the ACL in his right knee in Week 17 of the 2011 season and didn't return until Oct. 4 of last season. His return didn't last long, though, as he strained his right Achilles four days later.
The 25-year-old running back has rushed for 3,549 yards and 29 touchdowns in 57 career games.
The Cardinals released running back Beanie Wells last week.
The 6-foot-4, 229-pound Wells was envisioned as a power running back to anchor Arizona's offense, but injuries and inconsistent play kept him from being a regular threat. He had only three 100-yard rushing games in his four seasons in the desert.
Coming off his third Pro Bowl season as a member of the Cleveland Browns, Cribbs ranked fourth in the NFL in kickoff returns in 2012, averaging 27.4 yards per return. He also averaged 12 yards on punt returns.
Arizona has reached contract agreements other free agents, including quarterback Drew Stanton, who follow Arians to the desert.
Arizona also released starting free safety Kerry Rhodes, a move that cleared cap space to help accommodate the signings.
The other additions are cornerback Jerraud Powers, safety Yeremiah Bell and cornerback Lorenzo Alexander. Stanton backed up Andrew Luck last season in Indianapolis, where Arians served as offensive coordinator and as interim head coach.
Information from ESPN.com senior writer John Clayton and The Associated Press was used in this report.