The Bears and veteran quarterback Josh McCown have agreed to terms on a one-year contract.

McCown has been on the Bears’ roster the last two seasons and played in three games (two starts) during the 2011 campaign. He served as the third-string quarterback last season behind starter Jay Cutler and backup Jason Campbell but did not see any game action.

Campbell signed a two-year contract with the Browns, leaving a void at the backup position. McCown could compete for that role as he enters his 11th NFL season. The only other quarterback currently on the roster is Matt Blanchard.

McCown, who turns 34 in July, completed 35 of 55 passes for 414 yards with two touchdowns and two interceptions in ’11. For his career, McCown has completed 645 of 1,113 passes (58 percent) for 6,998 yards with 37 touchdowns and 44 interceptions. He entered the league in 2002 as a third-round round draft pick of the Arizona Cardinals.

The Bears released McCown prior to the start of last season but re-signed him in November as insurance after Cutler sustained a concussion. McCown’s contract expired at season’s end.