Baker was signed by the Bengals in March less than three weeks following his release by the Tampa Bay Buccaneers.
Baker will receive $300,000 from the Bengals, who will not have to pay the remainder of his $3 million salary.
Entering his ninth NFL season, Baker lasted only one season with the Buccaneers after signing three-year, $15.75 million contract. He recorded 33 tackles in 15 games in 2017 but had his effort questioned by the team.
Baker had five productive seasons with the Washington Redskins (2011-16) before signing with Tampa Bay.
The 30-year-old Baker has 12.0 sacks in 93 games (56) starts, including a career-best 6.0 to go along with 53 tackles in 2015 with the Redskins.
Baker also was hurt by a numbers game with the Bengals, who have an ample number of solid defensive linemen on the roster. Andrew Billings has been impressive during the preseason while Michael Johnson, Sam Hubbard and Jordan Willis all can play at defensive tackle.