The FA board approved a sudden-death format instead for the last-eight stage of the competition to be played over one weekend.
"This change adds to the excitement of the competition and will benefit the wider game in general," chief executive Martin Glenn on the governing body's website (www.thefa.com).
"In a demanding calendar and with increased pressures on fans, it is important we move with the times and consider new innovations...
"While fully respecting tradition and history, this new development will help the Cup retain its status as a much-loved and world-renowned competition."
Premier League managers have frequently lamented FA Cup replays, which often clashed with Champions League fixtures.
England manager Roy Hodgson said the move would take English football closer to a Premier League winter break, just like top divisions in France, Italy, Spain and Germany.
"I think it's all designed eventually to maybe providing that elusive winter break," Hodgson said.
"There's been no doubt that one of the stumbling blocks has often been 'hold on, you have all of these replays and you're asking us to cut our season down'. I think it's only positive that this sort of move has been made."
