Anheuser-Busch InBev NV on Wednesday won approval for its $100 billion-plus takeover of rival SABMiller PLC, ushering in a new world order for the beer industry.

Shareholders from both companies voted overwhelmingly in favor of the acquisition, one of the largest in corporate history. AB InBev will drop the SABMiller name and begin trading as a combined company Oct. 11.

The...