In September, customers living within a two-mile radius of the Killingbeck store were able to take part in a month-long trial and could order items such as pizza, chicken nuggets, fries, onion rings and ice cream via the Just Eat app.
The service proved so popular that it has now been rolled out to the Beeston supermarket. Stores in Wakefield and Scotland are also taking part.
Users of the app can place orders from the Asda Kitchen and purchase a 16" pizza for just Â£6 from November 19.
Dishes are cooked in-store and delivered directly to the customer's door.
Flavours include margherita, American Sizzler, pepperoni and Vegetable Supreme. There is also a Â£15 meal deal that includes any pizza, four sides, one soft drink, dessert and a dip.
The delivery service is available from 12pm daily.
The scheme will be rolled out to more stores nationally if it continues to be successful.