ESPN.com's John Clayton first reported the deal on Tuesday. Terms of the deal weren't available.
Thomas has been an integral part of the Colts defensive line rotation, and started seven games last season after three-time Pro Bowler Dwight Freeney suffered a season-ending foot injury in November.
Last season, Thomas had a career-high 55 tackles, one sack and 14 quarterback pressures. He also forced a fumble and knocked down three passes.
In four NFL seasons, all with the Colts, Thomas has 137 tackles, six sacks, two forced fumbles and one recovery.
Colts president Bill Polian has said the team considered this a good free-agency period because it had re-signed safety Bob Sanders, tight end Dallas Clark and guard Ryan Lilja before they could hit the open market.
Information for The Associated Press was used in this report.