Cesaire, 25, has proven to be a hard working, physical player at the point of attack and has made tremendous strides in his game since being signed as an undrafted free agent out of Southern Connecticut State in 2003.
Last year, Cesaire provided depth at the defensive end positions in the 3-4 and was also used as a defensive tackle to spell Jamal Williams. He ended the season with 25 tackles and a sack.
Locking up the 6-foot-2, 295-pound lineman ensures he will be with the team through 2010.
Financial terms were not immediately available and the deal is expected to be announced soon.