Terms of the deal weren't immediately disclosed.
A seventh-year veteran, Morgan, 28, finished last season with the Washington Redskins, catching 20 passes for a career-low 214 yards. Morgan was also among Washington's game day inactives twice last season, after a strong campaign in 2012 in which he led the Redskins with 48 receptions for 510 yards.
Perhaps a fresh start in Chicago can invigorate Morgan's career as he reportedly clashed in Washington with former Redskins coaches Mike Shanahan and Kyle Shanahan.
Having spent time with the San Francisco 49ers (2008-11) and Redskins (2012-13), Morgan caught a career-high 52 passes during his second season for 527 yards and three touchdowns.
With the Bears, Morgan will likely compete for a spot as the No. 3 or No. 4 receiver as well as for a role as a return man on special teams. He'll face competition from Domenik Hixon, Eric Weems, and Chris Williams for roles on special teams and one of the reserve receiver spots if he doesn't beat out rising second-year man Marquess Wilson for the No. 3 receiver position.
Morgan (6-1, 220 pounds) was originally drafted by the 49ers in the sixth round in 2008 out of Virginia Tech.