The deal follows FIFA's $90m (£45m) payout to settle its legal dispute with incumbent sponsor MasterCard, which claimed it should have been given first refusal on the deal.
The activity surrounding Visa's tie-up, which also includes the under-20 and women's tournaments, will be handled by Wieden & Kennedy, which has been handed responsibility for the brand's global World Cup ad account.
The agency picked up the £100m business in a pitch against RKCR/Y&R, TBWA\Chiat\Day, 180 Amsterdam and Saatchi & Saatchi London, which was put on hold during court proceedings.
Visa will become FIFA's sixth and final top-tier partner. It already has global sponsorship deals with the Rugby World Cup and the Olympic Games.