SYDNEY—Vegemite, Australia’s best-known condiment, is about to have something relatively unusual in its nearly 100-year history: an Australian owner.

The salty spread is among a basket of brands being sold by U.S. foods producer Mondelez International Inc. to Bega Cheese Ltd. for 460 million Australian dollars (US$348 million). They include peanut butter, processed cheese slices, Kraft Mac & Cheese and a license to the Dairylea brand in Australia and New Zealand.

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