Ogunjobi, 26, started all but two games for the Cleveland Browns over the past three seasons, compiling 13.5 sacks -- but only 2.5 in 2020.
Among interior defensive linemen, Ogunjobi, a third-round pick of the Browns in the 2017 draft, ranked 55th last season with a run block win rate of 29.5%. He was 37th in pass rush win rate. In 60 games over four seasons, he has 180 tackles, 14.5 sacks and two forced fumbles.
Ogunjobi gives the Bengals an interior pass-rusher to help a defense that finished 2020 last in the NFL in sacks. Earlier in the week, the Bengals agreed to terms with former New Orleans Saints defensive end Trey Hendrickson, who had 13.5 sacks last season.
The Ogunjobi signing could also be critical if the Bengals part ways with longtime defensive lineman Geno Atkins. Atkins, an NFL All-Decade Team selection, will give the Bengals $9.5 million in cap savings if he's cut.
ESPN staff writer Jake Trotter contributed to this report.