Peterson is signing a one-year, $1.05 million contract that includes incentives, a league source told ESPN's Adam Schefter.
The move reunites Peterson with his former offensive coordinator with the Minnesota Vikings, Darrell Bevell, and adds to an already crowded Lions backfield that includes Kerryon Johnson, last year's starter, and 2020 second-round pick D'Andre Swift.
"They're giving me an opportunity to play," Peterson, 35, told Anderson. "I know Coach Bevell from my days in Minnesota. Ultimately I feel comfortable going there and helping them to get better."
Peterson's move to Detroit comes days after Washington released him in favor of younger running backs. Now Peterson enters a room where four backs -- Bo Scarbrough, Ty Johnson, Kerryon Johnson and Swift -- are 23 or younger.
After his release, Peterson told ESPN's John Keim that he was surprised by Washington's decision and "without a doubt" wanted to continue playing. Peterson told Keim that based on what he showed in training camp, he can still contribute.
"We'll see what happens. ... Every new chapter is a blessing," Peterson said. "Whatever comes next, I'll be blessed to attack it. I can't be down on myself. I know it wasn't because of my ability or inabilities to do something. It came down to those guys making their decision."
Bevell coached Peterson at the beginning of his career. When the two were together with the Vikings from 2007 to 2010, Peterson rushed for at least 1,298 yards and 10 touchdowns each season. He made the Pro Bowl all four seasons they were together.
It has been a decade since they were last paired together, though, and Peterson has bounced around the NFL the past three seasons, playing in New Orleans, Arizona and Washington after 10 years with the Vikings.
Peterson has played in 164 games with 3,036 carries for 14,216 yards and 111 touchdowns. The seven-time Pro Bowler and four-time first-team All-Pro is fourth on the career rushing touchdowns list behind Emmitt Smith, LaDainian Tomlinson and Marcus Allen. He is fifth in career rushing yards behind Smith, Walter Payton, Frank Gore and Lions legend Barry Sanders, who is fourth with 15,269.
Sanders welcomed Peterson to the Lions in a tweet, writing "It will be great to have you in town."
Peterson will join an offense in which he might not be expected to handle a full workload.
"We always want a stable of backs," Lions general manager Bob Quinn said in April after the team drafted Swift. "I think I've said that for a long time. You can count on one hand how many backs kind of carry the load. There's not a lot of those guys walking around.
"I think we always need multiple backs. It's a position where guys get hit. They take a pounding. So we've just got to make sure we have good depth and guys that can go out there and make plays for us."
When the Lions were prepping to face Washington in 2019, Patricia was effusive in his praise of Peterson, showing his team a clip of a 90-yard Peterson touchdown run from 2018.
"The better backs or the veteran backs, they'll press that line of scrimmage longer," Patricia said of Peterson at the time. "They'll push that further up into where the offensive line blocks are occurring and then make their cuts or make their reads and do that more at the last second, and that becomes much more difficult. That's where you really see a guy like Adrian Peterson, who just feels so comfortable kind of getting all the way right there, and then he's going to make that cut and go. That's where he becomes really explosive, so that's kind of the danger part of what he does."
It's not immediately clear what the corresponding move will be for the Lions to make room for Peterson.