Anheuser-Busch InBev SA agreed to sell its Australian unit to Asahi Group Holdings Ltd., as the world’s biggest brewer tries to pare its heavy debt at a time when American beer drinkers have been losing their taste for the stuff.

AB InBev, which makes one out of every four beers sold world-wide, owns hundreds of brands in dozens of countries after a global buying spree that gave it Budweiser, Stella Artois and Corona. But those deals saddled the Belgian brewer with about $100 billion in debt; meanwhile, beer sales have slowed...