The governing body said in a statement on Monday that the deal would ensure the FA Cup's status "as the world’s original and greatest domestic cup competition".
No financial details were given but British media said the deal, which also includes rights for the Community Shield and FA Youth Cup, was worth about one billion pounds.
The FA has signed a memorandum of understanding with Pitch International to cover western Europe, the Middle East and North Africa and with IMG for the rest of the world.
The domestic rights stay with the BBC and BT Sport, with an agreement already in place to extend those deals through 2021.
"This is a hugely significant deal for The FA as a not-for-profit organisation," said chief executive Martin Glenn.
"It means we will be able to invest even more than we currently do in pitches, facilities and participation programmes to make football available for all.
"...it could have a transformational impact on what we are able to achieve across the country.
"It also underlines the global popularity of The Emirates FA Cup, with its history and tradition it has the remarkable ability to create fantastic stories and inspire fans, players and clubs to believe anything is possible."
The agreement comes after the FA allowed agencies such as Pitch International and IMG, and broadcasters to bid on single territories, regional groupings or a global package of rights.
(Writing by Ken Ferris; Editing by Andrew Both)
