Both sets of investors voted the deal through at respective general meetings, paving the way for the deal to complete on October 10.
The tie-up between the Budweiser owner and the brewer of Peroni and Pilsner Urquell will create the world’s biggest beer company.
Global regulators have already approved the creation of the enlarged group, which will make almost a third of the world's beer and will take the AB InBev title.
AB InBev had to raise its offer several times to get SABMiller to accept it and was forced to up the price again, by a pound to £45 per share, after the UK’s EU referendum vote in June hit sterling.
AB InBev chief executive Carlos Brito said: "We are committed to driving long-term growth and creating value for all our stakeholders."
Stella Artois brewer AB Inbev also makes Budweiser, Corona and Leffe, while Britain-based SABMiller - which holds second position - owns Peroni, Grolsch and Pilsner Urquell beers.
ABI employs about 1,000 people at its UK breweries in Magor, Samlesbury and Mortlake, as well as its company headquarters in Luton. It has at least 200 beer brands.
SABMiller has around 69,000 staff in more than 80 countries, from Australia, Zambia and Colombia to the Czech Republic, South Africa and the US, also producing more than 200 beers.
Formerly known as South African Breweries, SAB acquired US rival Miller Brewing Company in 2002, resulting in the renaming of the group as SABMiller.
A merged group would add AB InBev's dominance of Latin America to SABMiller's strong presence in Africa, as well as their breweries in Asia.