The deal is worth up to $2.7 million, a source told ESPN's Adam Schefter.
Daniels, 31, suffered through an injury-plagued 2019 season with the Detroit Lions after signing with the club at the start of training camp. Injuries to his foot and arm limited him to nine games, with two starts and one sack.
The Bengals signed Daniels to provide depth at defensive tackle. Ryan Glasgow was waived after he failed a physical, and Josh Tupou opted out of the 2020 season. On Tuesday, Bengals coach Zac Taylor declined to talk about Daniels until he officially signed his contract.
Before 2019, Daniels spent his entire career in Green Bay, where he played in 102 games, starting 72 as a defensive end or defensive tackle. He was valued as a strong player who could create pass rush from the interior of the defensive line, registering 30 sacks in his career.
A Pro Bowler in 2017, Daniels was listed on the NFL Top 100 list from 2016 to 2018 with the Packers.
ESPN's Michael Rothstein contributed to this report.