The agency was handed the business as the company prepares its high-profile launch into the Australian market.
Leo Burnett picked up the business following a four-way shoot-out against undisclosed agencies.
Melinda Geertz, the managing director of Leo Burnett Melbourne, said: "We're so very excited to be working with Unisnack. We've been talking to them for nearly two years now, but things really gathered momentum when they completed construction of their new plant in Australia earlier this year. All I can say is, expect a revolution in snacking."