Jerry was one of three offensive linemen named in the NFL's report into the Dolphins bullying scandal last season, with investigator Ted Wells finding that he joined Richie Incognito and Mike Pouncey in harassing teammate Jonathan Martin.
However, Giants general manager Jerry Reese insists that the team had looked into allegations about Jerry's character before they decided to add him to their roster.
"We did our homework on John, like we do with every player we sign. We were satisfied with the answers we got about John as a player and person," Reese said in a statement.
Jerry, 27, spent four years with the Dolphins having been picked in the 2010 NFL Draft, starting all 16 games at right guard in both of the past two seasons.