ESPNChicago.com reported on Sunday that Adams, 31, had been told he would be released by the Bears.
"Cuts are never easy, but are a part of the evaluation process," Bears general manager Phil Emery said in a statement. "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."
A ninth-year veteran, Adams played the first seven games of the 2011 season -- starting two -- but was inactive for five of the team's next eight outings. Adams hadn't been inactive in that many contests since the 2008 season.
Adams was scheduled to receive $1.9 million in base salary while counting $2.65 million against the Bears' salary cap.
Omiyale, 29, was a versatile lineman in his three seasons with the Bears, starting 31 games at both guard and tackle positions in 48 regular season games.