The team also re-signed offensive linemen Clint Boling and Eric Winston and cornerback Chris Lewis-Harris.
"It's a good day for us, a big day, and I compliment our front office for getting these deals done," said Bengals coach Marvin Lewis. "It's a continuation of the building process to keep getting better, the plan to retain the core players who have gotten us to the playoffs and add new talent in the right spots."
Hawk spent the past nine seasons with the Green Bay Packers. Last season, Hawk played 16 games (13 starts) and recorded 89 tackles. The Ohio State product tallied 921 tackles, 19 sacks and nine interceptions in 142 career games with the Packers.
"As for our new guy, A.J. (Hawk), he has been productive for a long time at the highest level, and we think he can fit for us at all three of our linebacker positions," said Lewis.
The 31-year-old Winston, who is the president of the NFL Players Association, was signed by the Bengals on Dec. 2 and appeared in their final four regular season games, helping them clinch a playoff berth.
He was signed by Seattle last July but was cut a month later before the season started and was out of the league until the Bengals picked him up.
Winston has spent most of his career with Houston, also playing for Kansas City and Arizona, and he started 16 games for seven consecutive seasons from 2007-13.
Boling has started 47 games for the Bengals over the past four seasons. He started every game last season.
Lewis-Harris has played in 12 games for the Bengals over the past three seasons.