While there is no minimum spend for the service, customers can only order a maximum of 20 products.
Shoppers have been able to pick up Morrisons products during the coronavirus crisis through Amazon.
Amazon Prime members can get same day delivery on these products when they spend more than £40.
The full range of Morrisons products is available to order in Leeds as part of a trial, but other locations can still choose from a limited selection of items.
Tesco offers same-day delivery for customers who order before 1pm, according to a statement on its website.
Customers can check if there is a slot available that day by looking on the website.
Shoppers can choose from 300 own-brand Asda products and order on the Uber Eats app for delivery in as little as 30 minutes.
Vice president of online grocery at Asda Simon Gregg said: “We’re pleased to be partnering with Uber Eats to trial a rapid grocery delivery service for customers in Leeds and Birmingham.
“This will give Asda customers more choice in how they shop with us and offer yet another way to quickly and conveniently get their favourite branded and own-brand products delivered to the doorstep.
“Customers can use the Uber Eats app to select from hundreds of items for delivery in the same way they would shop for a takeaway.”