Gilberry was signed as a free agent last September and finished third on the team with 6 1/2 sacks. He also recovered three fumbles and returned one for a touchdown, becoming an integral part of Cincinnati's rotation on the line.
Geathers has spent all of his nine seasons in Cincinnati, making him the longest-tenured Bengal. He had 3 1/2 sacks.
Earlier this month, the Bengals used their franchise tag on end Michael Johnson, who had 11 1/2 sacks last season. Johnson will be paid more than $11 million this season if he doesn't reach a long-term deal.
The line was the strength of a defence that ranked sixth in the NFL.