Although the Patriots did not release terms of the deal, the Browns announced that they sent Shelton and a fifth-round pick in the 2018 NFL Draft to New England in exchange for a third-round selection in 2019.
Shelton, 24, has recorded 71 tackles and 1.5 sacks in 46 career games since being selected by Cleveland with the 12th overall pick of the 2015 NFL Draft. He had 34 tackles in 14 contests (13 starts) last season.
The 6-foot-2, 335-pound Shelton is slated to earn a base salary of $2.03 million in 2018.
Shelton could aid the Patriots after the team declined to pick up the contract option on defensive tackle Alan Branch, making him a free agent.
Branch, 33, joined New England in 2014 and was a key contributor during the 2015 and 2016 seasons, appearing in all 32 games and making 30 starts.