Rivals such as Morrisons, Tesco, and Sainsbury’s already offer one-hour delivery via other providers such as Deliveroo, Uber Eats, and Amazon.
However, they do not offer a full range of products.
Rapid delivery is the latest frontier in the battle for grocery shoppers’ cash.
At £8.50 per delivery, the cost is higher than their rivals’ services.
The scheme is currently limited to a three-mile radius of its stores in Halifax, Rotherham, and Poole, where it is being trialled.
If popular, the scheme, announced on June 30, will be rolled out to other stores.
Customers can have either a maximum of 70 items delivered in an hour, or unlimited basket items within four hours.
Simon Gregg, Asda’s vice president of online grocery, said in a statement, “After successfully trialling an Express Delivery service, we know this is something that our customers want as part of our online grocery proposition and we are delighted to be able to offer this service to even more customers.
“The launch of our new Express Delivery service and extension of our existing partnership with Uber Eats to 300 stores means that customers can get their order delivered to the doorstep at market-leading pace.”
Most UK supermarkets are trying to crack the delivery market, to get groceries to customers more quickly, on demand.
A raft of new firms, including Weezy, Getir, Dija, and Gorillas, are offering deliveries within 15 minutes of ordering, prompting traditional supermarket groups to rethink their business models.
Earlier this month Tesco extended a one-hour delivery trial as it tests consumers’ appetite for the service.
Sainsbury’s also expanded its own service, called Chop Chop, to 50 stores in 20 cities last year.
Waitrose says it is now expanding its partnership with Deliveroo and will shut down its own rapid delivery service that lasted just two years.
Morrisons offers same-day rapid deliveries as part of its tie-up with Amazon, which also offers customers its own Amazon Fresh products.
Asda is third in annual sales after market leader Tesco and Sainsbury’s. Together with Morrisons, they make up what is sometimes called the “Big Four,” worth two-thirds of the grocery sector by market share in the UK.
Asda is also extending its partnership with Uber Eats from 200 to more than 300 stories.
Reuters and PA contributed to this report.