A week after Manchester United lift tropy FA scap quarter-final replays
The Football Association said the decision to scrap quarter-final replays was part of its "ongoing review" of the competition and helped to "ease English football's congested fixture schedule".
Semi-final replays were phased out after Manchester United's 1999 victory over Arsenal on their way to winning the treble.
FA chief executive Martin Glenn said the change "adds excitement".
Replays in earlier rounds remain, meaning lower-league clubs will still have the opportunity to earn lucrative second matches against higher-ranked clubs.
Manchester United beat West Ham in a replay in this season's quarter-finals - Marouane Fellaini scoring the winning goal - before going on to lift the trophy in the final at Wembley.
Glenn added: "While fully respecting tradition and history, this new development will help the cup retain its status as a much-loved and world-renowned competition."