According to the report, Morris will coach the Falcons' pass defense.
The New York Giants and Redskins were reported interested in Morris as a potential defensive coordinator.
Morris, who spent the last three seasons as defensive backs coach with the Redskins, is expected to coach under Seattle Seahawks defensive coordinator Dan Quinn, who reportedly will be named the Falcons' next head coach as soon as the Seahawks finish playing in the Super Bowl on Sunday.
Morris was head coach of the Tampa Bay Buccaneers for three seasons from 2009 through 2011, compiling a 17-31 record in his tenure.
Last season, the Falcons were last in the NFL in passing defense, allowing 8.2 yards per attempt and 280 yards per game.
- Scooby Axson