The 31-year-old had surgery after the season to remove bone spurs in his ankle. He played all 16 games last season, starting 13, and recorded 89 tackles and 0.5 sacks.
Hawk appeared in all but two of the 144 regular season games the Packers played during his time there. He has recorded 916 tackles in his career and is Green Bay's all-time leading tackler.
The linebacker has registered 100 tackles in five of his nine NFL seasons, most recently in 2013.
Hawk was born in Kettering, Ohio, and attended college at Ohio State.
Cincinnati's defense ranked No. 22 last season in total yards allowed.
- Molly Geary