Billings’ agent announced the agreement.
NFL Network reports it’s for one year and $3.5 million, fully guaranteed.
"Excited for this next chapter @Browns!," Billings tweeted.
Billings was drafted in the fourth round of the 2016 NFL draft by Cincinnati where he started 37 of the 47 games he appeared in for the Bengals.
In the three seasons since not playing his rookie year after tearing his meniscus during training camp, Billings totaled 80 tackles, 14 tackles for loss, 12 quarterback hits and 3.5 sacks.
Billings joins starters Sheldon Richardson and Larry Ogunjobi on the interior of the defensive line.
Billings becomes the fifth free agent to reach agreement with the Browns and sixth new addition by executive vice president of football operations and general manager Andrew Berry since the legal tampering window opened Monday afternoon.
On Monday, Cleveland agreed to contracts with right tackle Jack Conklin, quarterback Case Keenum and tight end Austin Hooper. Tuesday Berry added fullback Andy Janovich from Denver in a trade and on Wednesday safety Karl Joseph and linebacker B.J. Goodson agreed to contracts.