BBC One will broadcast the competition, with live streaming available across online, mobile and tablet devices.
"Bringing the FA Cup back to the BBC was something I really wanted to do," said BBC director general Tony Hall.
"I am so pleased that we have achieved it for football fans everywhere," Hall added.
"There is something very special about big national moments on the BBC and the FA Cup should absolutely be one of them.
"The Olympics, Wimbledon and Glastonbury have shown how our audiences love it when we put the full weight of all our services on TV, radio and digital behind covering these events in depth and in ways no-one else can.
"Working closely with the FA I believe we will change the way we view the FA Cup forever."
The deal was announced at Wembley Stadium earlier this week. Details of how many games will be shown live by the BBC have yet to be released. Radio coverage of the FA Cup also continues on BBC Radio 5 live until 2018.
Gary Lineker, who will lead the BBC presentation and was involved in the pitch to win the rights, said at Wembley: "It is terrific news. We have the European Championships, World Cup, Confederations Cup and we've got the Women's Euros 2013.
"These are summer events. In between Match of the Day is great with highlights every week, but this gives us regular, big live football on the BBC right throughout. It is so important and, vitally, fills a gap for us.