Sean Stellato of the SES agency confirmed details of the deal Thursday to Adam Schefter of ESPN.
He racked up 32 combined tackles, 3.5 sacks and a forced fumble across 16 appearances, including two starts, during his first season with New England. Pro Football Focus graded him as the league's No. 54 overall linebacker.
Flowers downplayed the lackluster PFF mark after the season:
"Marquis has done a nice job for us," Belichick said. "As he's gained more experience and confidence in our system, we've been able to do more with him. He's been very productive for us."
Flowers' role should remain pretty much the same in 2018. He'll serve as a reserve at linebacker behind Kyle Van Noy and Dont'a Hightower while also playing on special teams.