Bray, 27, returns to the Bears as their third-string quarterback, adding depth behind starter Mitchell Trubisky and backup Chase Daniel. He spent 2018 with Chicago but didn't play in a game.
A California native and University of Tennessee product, Bray has been in the NFL since 2013 but has played in just one game, attempting one pass. He has a familiarity with coach Matt Nagy's offense, having played under Nagy's watch in Kansas City for five seasons.
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The Bears also officially re-signed punter Pat O'Donnell on a two-year deal that has been reported to be worth $4 million.