To make room for Peterson on the roster, the Cardinals released running back Chris Johnson.
"We are always on the lookout for opportunities to improve our team and we look at this as one of those opportunities," general manager Steve Keim said in a statement. "What Adrian has accomplished in this league is well-established. Our need for a spark in our running game right now is also obvious and we are excited to give him the chance to provide that."
The Saints will receive a conditional 2018 sixth-round pick from the Cardinals in compensation, league sources told Schefter.
The Cardinals' running game has been a major weakness since David Johnson suffered a fractured wrist in Week 1. Arizona is last in the NFL in rushing yards per game (51.8) and per carry (2.59).
The team signed Chris Johnson after Week 1 to complement Kerwynn Williams, Andre Ellington and Eli Penny, but injuries to the left side of Arizona's offensive line have prevented the Cards' running game from finding its footing.
Peterson, 32, had 27 carries for 81 yards -- an average of 3.0 yards per carry -- in four games during his first season with the Saints (2-2). His longest run was 11 yards.
Peterson's addition comes 10 years after the Cardinals passed over him in the 2007 draft to select tackle Levi Brown with the fifth pick. The Minnesota Vikings drafted Peterson at No. 7, and he went on to rush for a franchise-best 11,747 yards.
Glad to see AP get a chance to show he's still got it and trust me he's still got it go flourish OG— rafael bush (@rbush36) October 10, 2017
Peterson's 3.0 yards per rush are still better, however, than the Cardinals players with the most carries this season. Chris Johnson averaged 2.5 yards on 45 rushes, and Williams has averaged 1.7 on 19 rushes.
Peterson needs 485 yards to become 10th-leading rusher in NFL history. He hasn't scored a touchdown this season, but if he scores three, he will become the ninth player to reach 100 rushing touchdowns.
He agreed to a two-year, incentive-laden deal with the Saints about a week before the draft, which included only $3.5 million guaranteed. But coach Sean Payton hinted recently the Saints might not have felt the same need to sign Peterson if they knew they would land Kamara in the draft.
Ingram leads the Saints with 42 carries for 170 yards and no touchdowns, plus 15 catches for 125 yards. Kamara has 15 carries for 83 yards and a touchdown, plus 20 catches for 147 yards and a touchdown.
Peterson admitted last week that he was frustrated with his ever-shrinking role in New Orleans because of "the type of player that I am, knowing I have so much left in the tank."
But he also continued to insist there was no animosity between him and Payton -- and that the infamous sideline glare that was captured on video in Week 1 was overblown and not what it looked like.
"When you're a competitor like I am, you're angry when you're not in there. But you're happy for the guys that are in there when they're being successful and able to accomplish good things," Peterson said last week. "So at the end of the day, I know that things will work out in some type of way. I don't know how things will unfold. But things will get figured out."
Peterson said after that Week 1 game that he knew what he signed up for in New Orleans -- joining a time-share in a crowded backfield for a pass-first team. "I didn't sign up for nine snaps, though," Peterson said at the time.
Peterson was hoping he would be able to take advantage of fewer eight- and nine-man fronts in New Orleans and expand his versatility as a pass catcher. But that role never materialized.
ESPN Saints reporter Mike Triplett and ESPN Stats & Information attributed to this report.