Terms were not disclosed. Offensive lineman Jake Eldrenkamp was released in a corresponding move.
The Patriots acquired Shelton and a 2018 fifth-round draft choice from the Cleveland Browns in exchange for a 2019 third-round pick last March. The deal was sparked, in part, because the 6-foot-2, 345-pound Shelton wasn't viewed as a scheme fit in the Browns' revamped 4-3 defense.
The Patriots projected Shelton's strength against the run might be a better fit in their multiple defense, and the results turned out to be up-and-down. The club didn't pick up the option for his contract for 2019, which would have paid him about $8 million.
The club kept four defensive tackles on its roster last season and is positioned to do so again this year, with starters Lawrence Guy and Mike Pennel atop the depth chart, followed by third-year player Adam Butler, Shelton, four-year veteran David Parry, and 2019 fifth-round draft pick Byron Cowart. So Shelton, who played 31 percent of the defensive snaps last season as a backup, will likely be competing for a roster spot with Parry and Cowart.
Shelton played in 13 regular-season games (one start) for the Patriots in 2018, totaling 21 tackles. He had been a healthy scratch for three straight games late in the season, as well as the AFC Championship Game against the Kansas City Chiefs, before playing one of his best games in Super Bowl LIII against the Los Angeles Rams.
Shelton, who turns 26 on Aug. 20, entered the NFL as a first-round draft choice of the Browns in 2015.
ESPN's Mike Reiss contributed to this report.