The team held a workout for Gradkowski at its training facility in Berea, Ohio. He last played for the Tampa Bay Buccaneers and has 17 games of NFL experience.
Cleveland was searching for a backup to play behind new starter Ken Dorsey, who entered the year as the third-string quarterback. The Browns also lost Brady Quinn recently with a season-ending finger injury.
Sunday the Browns will travel to Nashville to play the Tennessee Titans (11-1).
James Walker covers the AFC North for ESPN.com.