The veteran defensive lineman joined the Browns' roster on Wednesday.
Davis was drafted in the fifth round of the 2010 NFL Draft by the St. Louis Rams, and signed a four-year, $1.97 million contract with the Rams. He was traded to the Washington Redskins on the eve of the 2010 season, and was immediately released. He then joined the Tennessee Titans' practice squad, and spent the next year in Nashville before being released before the 2011 season. Davis later spent some time with the Oakland Raiders, and was waived immediately before the start of this campaign.
Davis is a natural defensive end, and recorded eight sacks in his final two seasons at Louisiana-Lafayette. He made one appearance in the 2010 season for Tennessee, but did not record a tackle.
Cleveland hosts the Baltimore Ravens on Sunday, with kickoff set for 1:00 p.m. ET.