The Giants announced the deal in a release Friday afternoon, referring to Jerry as an addition to the team's "new-look offensive line."
Richie Incognito, Mike Pouncey and Jerry were cited by Wells last month as players who participated in "a pattern of harassment" against Dolphins teammate Jonathan Martin, who left the team in October.
"We did our homework on John, like we do with every player we sign," Giants general manager Jerry Reese said in a statement. "We were satisfied with the answers we got about John as a player and person."
Martin was traded to the San Francisco 49ers earlier this month, and Incognito remains an unrestricted free agent. Pouncey, a Pro Bowl center, remains on Miami's roster.
Jerry, 27, started all 16 games at right guard in each of the past two seasons for the Dolphins. The 349-pound Jerry, who also has played offensive tackle, appeared in 57 games over his four-year career with Miami.