Defensive line coach Jacob Burney and linebackers coach Jim Haslett were with Baker in Washington from 2011-14.
"[The two men] groomed me and really believed in me," the 30-year-old Baker told the Bengals' website.
Burney has a high opinion of Baker, but cautioned that history "doesn't mean anything" if he isn't dedicated to football.
"I know the type of player that I am capable of being if I am given the opportunity to go out there and show what I can do," Baker said. "I know I can return to being one of the best defensive tackles in this game. I'm working my butt off each and every day and now that I'm with a coaching staff that believes in my ability, I'll show everybody what I can do."
Baker had five productive seasons with the Washington Redskins (2011-16) before signing a three-year, $15.75 million contract with the Tampa Bay Buccaneers prior to last season. He recorded 33 tackles in 15 games and had his effort questioned before being released by the Buccaneers on Feb. 18.
"I didn't play as well as I needed to play and didn't play to the standard that I know I can play at," Baker said, who signed a one-year, $3 million contract with the Bengals.
"But I'm happy to be here and have a fresh start. I'm in the best shape of my life. I'm down to 305 and I haven't been this light since college."