Adams is coming off the worst year of his career, recording just 16 tackles in 11 games for the Bears in 2011.
During his nine-year NFL career with the San Francisco 49ers (2003-06) and Chicago (2007-11), Adams has recorded 278 tackles, 10 1/2 sacks, four forced fumbles and three fumble recoveries in 121 games (74 starts).
Omiyale appeared in every game for the Bears during the last three seasons. The seven-year veteran played for Atlanta and Carolina before joining the Bears.
"Cuts are never easy, but are a part of the evaluation process," Bears general manager Phil Emery said. "We appreciate all that Anthony and Frank gave the Bears organization both on and off the field during their time in Chicago. We wish them the best moving forward."