The retail giant is initially trialling the Whoosh delivery service at one store and will then assess potential opportunities to expand the model.
It said the one-hour service will be available for customers in selected postcodes around its Wolverhampton Willenhall Express store.
The supermarket chain has seen soaring online growth during the pandemic but has so far refrained from following rivals into the on-demand grocery space.
Sainsbury’s operates its own Chop Chop rapid delivery business, as well as services through Deliveroo and Uber Eats.
Meanwhile, Waitrose recently scrapped its own Zoom rapid delivery business in favour of expanding its tie-up with Deliveroo.
A raft of major grocery retailers, including Morrisons, Aldi and the Co-op, also use delivery operators such as Deliveroo and Uber Eats to reach customers.
Tesco said customers will now be able to order on-demand via its app or Tesco.com, with products delivered by bike, moped or car, with a £5 delivery fee.
Chris Poad, online managing director at Tesco, said: “Customers are telling us that they would welcome the addition of a 60-minute delivery to their door option as part of our online grocery service.
“We’ll use the pilot to understand how Whoosh could work best for both our customers and our colleagues.”