Billings, 25, developed into one of the Bengals' most reliable interior linemen over the past three seasons, missing just one game over that span.
"Excited for this next chapter @Browns!" Billings tweeted.
Also Thursday, the Browns reached a one-year, $3.5 million deal with former Bills and Texans cornerback Kevin Johnson, a league source told ESPN's Adam Schefter. The deal could go up to $6 million with incentives, the source said.
In 2019, he made 14 starts and tallied 35 tackles, with four of them coming behind the line of scrimmage. Despite his presence, the Bengals struggled against the run, finishing last in the league in rushing defense.
Billings, a fourth-round pick out of Baylor in 2016, missed his entire rookie year because of a knee injury suffered just before the season.
Overall, Billings has 80 tackles and 3.5 sacks in his three seasons.
ESPN's Ben Baby contributed to this report.