The move will see the US brewing giant’s brands, including Budweiser and Michelob, join the Inbev portfolio.
The agreement came after friendly talks between the two parties ended a period of hostile public exchanges.
Inbev secured victory after increasing its initial offer which valued Anheuser at around $46 billion.
The move creates the world’s biggest brewer and one of the top five consumer products groups globally.
Anheuser’s St Louis, Missouri, base will become the headquarters for Inbev in North America and the global home of Budweiser.
All of Anheuser’s US breweries will remain open as part of the deal, which values Anheuser at $52 billion.
Anheuser president and chief executive August Busch IV will join the board of the combined company headed by Inbev chief executive Carlos Brito.
Brito said: “Together, Anheuser-Busch and Inbev will be able to accomplish much more that each on its own.
“This combination will create a stronger, more competitive global company with an unrivalled worldwide brand portfolio and distribution network, with great potential for growth all over the world.”
Budweiser will become a lead global brand for the combined company alongside Stella Artois and Beck’s.