TOKYO—Uber Technologies Inc. plans to launch its food-delivery business in Tokyo on Thursday, preparing for a gradual rollout across Japan—a country where its main ride-hailing business is barred.

In a city where good restaurants are plentiful but delivery isn’t always available, UberEats bicycle couriers will carry dishes from more than 150 restaurants whose offerings range from inexpensive comfort food to high-end Michelin-starred fare.

Food...