Hicks was released by the Washington Redskins on Saturday. The 6-foot-4, 325-pounder has played nine seasons in the NFL, making 68 starts, including 27 at left guard.
The Browns have a hole at that position after losing Eric Steinbach for the season following back surgery.
Hicks will likely compete with rookie Jason Pinkston for the starting job.
Hicks was originally signed as an undrafted free agent by Philadelphia in 2002. he was traded to Minnesota before the 2006 season.
Last season, Hicks played in 15 games and started 10 games at right guard for the Redskins.