Ballard suffered a torn ACL in the Giants' Super Bowl XLVI win over the Patriots, and is expected to miss part or all of the 2012 season.
By claiming Ballard, the Patriots likely will keep him on their active roster until placing him on the "physically unable to perform" list or injured reserve before the start of the regular season.
In a statement released by agent Blake Baratz, Ballard said on Tuesday: "While this was very sudden and I am still experiencing a great deal of differing emotions, I wanted to take a moment to say Thank You and place some closure on a wonderful chapter in my life. I will greatly miss my teammates, the fans, the organization, and albeit short-Iived, I will forever cherish all the great memories that we created during my time in a Giant uniform. Simultaneously, I am humbled by the opportunity that the Patriots have afforded me and as I have always done, I will bring nothing but hard work, professionalism, and integrity to what is already a world class organization."
The Patriots now own Ballard's rights, and inherit his one-year, $540,000 contract. In his second year with the Giants, the 24-year-old Ballard had 38 receptions for 604 yards and four touchdowns in 14 games. He will be an exclusive-rights free agent after this season, meaning the Patriots will control his rights heading into the 2013 season.
In 2010, the Patriots claimed safety Josh Barrett after he was waived/injured by the Broncos. They stashed him on injured reserve that season before he returned to the Patriots in 2011, starting four games.
Mike Rodak contributes to ESPNBoston.com's Patriots coverage.