The 35-year-old Thomas missed the first half of the 2008 season after hurting his triceps in training camp. He made 10 tackles in the Saints' final eight games.
Thomas came to the Saints in a draft-day trade from Philadelphia in 2006 and has made 117 tackles with 61/2 sacks and a fumble recovery in his three seasons in New Orleans.
Saints coach Sean Payton called him "a significant presence" both on the defensive line and in the locker room and that he was "a big part of what we have accomplished here."
Thomas, a 13-year NFL veteran, spent his first 10 seasons with the Eagles.
