Last season, the five-year NFL veteran struggled when he was made a nose tackle in the Dallas Cowboys' 3-4 defensive scheme and was not re-signed. In 16 games last season in a backup role he made 22 tackles with one sack.
"In the 3-4, nose tackle wasn't really his thing," Bengals' defensive coordinator Mike Zimmer told The Cincinnati Enquirer. "Playing in a three technique gives him greater flexibility to play both sides."
The five-year veteran, a second-round draft pick by the Chicago Bears out of the University of Washington in 2004, was released by Chicago following his arrest for violating probation on a gun charge. The violation carried an eight-game NFL suspension.
In 70 NFL games, Johnson, 27, has 96 tackles and 12 sacks.
"The addition of Tank will increase our ability to apply pressure on the football," Cincinnati Coach Marvin Lewis said in a statement.