Redman had been with the Falcons since 2007 and worked as the backup during each of Matt Ryan's first four seasons. But Redman was unimpressive in his preseason outings and the Falcons have been delighted with the play of undrafted rookie quarterback Dominique Davis.
McCown, who was recently released by the New Orleans Saints, spent the last three seasons in Jacksonville where new Atlanta offensive coordinator Dirk Koetter held the same position.
Although the Falcons may go with Davis as their No. 2 quarterback, adding McCown, who has made nine career starts, gives them another option with experience.