The Giants confirmed the move later Friday.
Jones started the first two weeks of the 2011 campaign before moving to a reserve/spot starter role for the remainder of the regular season. The 6-foot, 248-pound linebacker had 31 tackles, including six on special teams. Official playing-time documents show that Jones played in nearly 70 percent of the snaps.
Because Jones was active for all 16 games last season, he is ineligible for the practice squad.
"It was fun working with a great organization like the giants and for y'all giant fans I could only imagine if I started my career here," Thomas wrote on Twitter.
An 11-game starter for the 2011 Denver Broncos, Thomas -- who was misidentified in "Madden NFL 13" -- joined the Giants earlier this month when injuries depleted the depth along the interior of the defensive line. It's possible the Giants would bring Thomas back after the start of the regular season.Follow Brian McIntyre on Twitter @brian_mcintyre.