"I'm back with people who believe in me. Happy to move forward," Baker told ESPN's Josina Anderson on Wednesday.
The Bengals hosted Baker for a visit earlier this week. Baker, 30, was cut by the Tampa Bay Buccaneers on Feb. 20 just one season into a three-year, $15.75 million contract that he signed last March. He had only half a sack last season.
The agreement is the second the Bengals have reached this offseason. They signed offensive lineman Bobby Hart to a one-year deal after he was cut by the Giants. The Bengals also were one of several teams that pursued free-agent safety Kurt Coleman before he signed with the New Orleans Saints last week.
The Bucs had signed Baker to a three-year deal worth $15.75 million last offseason to be an upgrade at the defensive tackle position over Clinton McDonald.
Baker registered just 33 tackles, a half-sack and two passes defensed in 2017. McDonald, meanwhile, tallied five sacks in just three starts.
While Baker, 30, was considered a fun personality in the locker room, his effort in practice was a source of concern, as it was during his time with the Washington Redskins, with whom he spent five seasons.
Things reached a boiling point in Week 16, when Tampa Bay teammates Jameis Winston and Kwon Alexander confronted Baker over his lack of remorse following a costly penalty that led to the Carolina Panthers' game-winning touchdown.
ESPN's Jenna Laine contributed to this report.