McCown is expected to enter training camp as the No. 3 quarterback. Second-year quarterback Nate Enderle is also under contract with the Bears.
McCown appeared in three games for the Bears last season, starting the final two. He completed 63.6 percent of his passes and threw for two touchdowns and four interceptions.
McCown, 32, has started 33 of his 50 NFL games played in nine seasons with the Arizona Cardinals (2002-05), Detroit Lions (2006), Raiders (2007), Carolina Panthers (2008-09) and Bears (2011) after entering the league as a third-round selection by Arizona in the 2002 NFL draft.