SABMiller said investors backed AB InBev's £45-a-share offer, which was upped from £44-a-share in July following the collapse in the value of the pound after the Brexit vote.
The record-breaking deal - dubbed "megabrew" - is now set to complete on 10 October, creating a brewing giant with a raft of some of the world's biggest beer brands.
SABMiller said 95.5% of minority investors approved the deal. AB InBev needed at least 75% to clinch the takeover.
The two largest shareholders in SABMiller - cigarette maker Altria Group and the wealthy Santo Domingo family of Colombia, which together control around 40% of shares - were excluded from the vote, but had already pledged their support for the deal.
Investors in Belgium-based AB InBev also approved the takeover at a meeting in Brussels earlier on Wednesday.
AB InBev said it welcomed the shareholder backing.
Carlos Brito, chief executive of AB InBev, who will also lead the merged group, said the deal will combine the two firms' "teams, strong heritage and passion for brewing".
"We are committed to driving long-term growth and creating value for all our stakeholders," he added.