Further details of the deal are not yet known.
Davis has spent his entire four-year career with the Bears, but the team released him earlier this month after a season that saw him catch just 19 passes. Tight ends will figure prominently in new Cleveland coach Rob Chudzinski's offense, though Davis will likely be relegated to a blocking role.
The Browns recently signed free-agent tight end Gary Barnidge and reportedly are interested in Washington's Fred Davis. Ben Watson, a three-year starter at tight end for Cleveland, signed with the Saints earlier this week.
For his career, Davis has 47 catches and 11 touchdowns.