Limiting the selection of products to 70 “essential” household items, including fruit and vegetables, bread, milk, chicken soup, Pringles crisps and Crunchy Nut cornflakes.
Items will be priced at the same price as in stores, the FTSE 100 group said, with delivery limited to those who live within 2.5 miles of a store.
Delivery by bike will be charged at a flat £4.99 fee, unless customers have the Deliveroo Plus service.
Morrisons chief executive David Potts said: “Our partnership with Deliveroo will help us to continue to play our full part in feeding the nation.”
A surge in extra shopping and some hoarding due to the coronavirus outbreak meant March was the biggest month of sales on record for the UK grocery industry, with online grocery spend surging 13% compared to this time last year.
However, online capacity has been constrained by lack of delivery vans, meaning it is difficult for households to find available delivery slots.