The move was expected for Peterson, who was acquired by the Cardinals last season and made six starts before landing on injured reserve with a neck injury.
Peterson, who will turn 33 on March 21, became expendable because star running back David Johnson is expected to be fully healthy for Arizona after suffering a season-ending wrist injury in Week 1 of the 2017 season.
Peterson rushed for more than 1,200 yards in seven of his 10 seasons with the Minnesota Vikings, including a career-best 2,097 in his MVP campaign in 2012. He also rushed for 97 of his 99 career touchdowns with the Vikings.
Minnesota declined to pick up Peterson's option for the 2017 season and he signed a two-year contract with the Saints last April.
Peterson was No. 3 on the depth chart in New Orleans, rushing for just 81 rushing yards on 27 carries over four games before he was shipped to Arizona.
He racked up a pair of 100-yard games for the Cardinals and finished as the team's leading rusher with 448 yards and two touchdowns in six games.