The contract is worth up to $13.6 million, a source told ESPN's Adam Schefter. About $6 million of the deal is tied to incentives, a source told ESPN's Mike Reiss.
Newton posted a video on Instagram later Friday with a caption that read in part, "Run it back!! Chapter 2."
Newton, who will turn 32 in May, hoped to return to New England after signing a modest one-year deal with the team in 2020. On the "I Am Athlete" podcast in late February, he said he would be open to another one-year deal in New England.
"I'm getting tired of changing [teams]," the quarterback said. "I am at a point in my career where I know way more than I did last year. Yes, I would go back."
In 2020, Newton was 242-of-368 for 2,657 yards passing, with 8 touchdowns and 10 interceptions. But while that production didn't meet his personal standard -- in part because the receivers and tight ends around him weren't high-caliber options -- he was effective as a rusher, with 592 yards on 137 attempts (4.3 yards per carry) and 12 touchdowns.
Newton had started hot in 2020 after joining the Patriots in late June, but after testing positive for COVID-19 in early October, he said it was a challenge for him to catch up to the pace of the team's ever-evolving offense. His performance dipped notably, and he said it reinforced how important it is to be with a new team in the offseason.
The Patriots went 7-8 with Newton at the helm and finished 7-9, missing the playoffs for the first time since the 2008 season.
Before joining the Patriots, Newton, the No. 1 pick in 2011, was released by the Carolina Panthers after missing 14 games in 2019 with a Lisfranc injury and the final two games of the 2018 season with a shoulder injury that also required surgery.
He spent nine seasons with the Panthers and was named the NFL MVP in 2015, when he accounted for 45 total touchdowns in the regular season and led Carolina to Super Bowl 50, where it lost to the Denver Broncos.
Newton, who holds most of Carolina's career passing records, has thrown for 31,698 yards and 190 touchdowns with 118 interceptions and has rushed for 5,398 yards and 70 touchdowns.
The Boston Globe first reported news of Newton's return to the Patriots.