The three-year deal will see the competition known as the FA Cup with Budweiser.
A portion of the sponsorship money will be put towards a programme to promote responsible drinking to football fans.
Money will also go into an initiative to provide equipment to non-league teams in the early rounds of the competition.
Alex Horne, FA general secretary, said: “Given the global reach of this sponsorship, we will see the FA Cup promoted around the world like never before which is great for the fans and the players.
“The FA Cup is already a much-loved competition around the world and we look forward to building on that passion with Budweiser.”
Chris Burggraeve, chief marketing officer at AB Inbev, said: “AB Inbev is a long-standing supporter of football around the world. We share the FA’s ambitions to showcase the tournament globally."