People will be able to order Argos products online, and then collect them in the supermarket locations the same or the following day, Argos said.
Sainsbury's has seen strong demand for non-food products over the past three years.
And in November it found that 6% of shop-floor space was being under-used.
The supermarket giant aims to fill half of that space with clothing lines, and devote half of the space to general merchandise.
"These 10 Argos stores will complement our supermarket offer, giving customers the opportunity to shop for an extended range of non-food items," said Mike Coupe, chief executive of Sainsbury's.
Argos customers can already order products online to be delivered by post, or can opt for so-called 'click-and-collect' - which Argos calls 'check and reserve'.
Check and reserve is important to Argos - it accounts for a third of Argos' total sales.
The digital pilot, which will be in 10 Sainsbury's supermarkets with a floor space of between 30,000 to 100,000 square feet, will be in shops dotted around the UK.
Possible locations of the concessions have been identified, and should be announced within the next few weeks, a Sainsbury's spokeswoman said.
The concessions are likely to be located in areas which are further away from existing Argos shops.
Around 1,000 products will be held in stock in the supermarket, and about 20,000 products will be available to collect the same or following day. Products that are not held in the supermarket will be delivered from one of 140 larger Argos stores.
Argos has ten concessions in Homebase DIY stores - both companies are part of the Home Retail Group.
Sainsbury's already has concessions from around 30 different firms in its shops.
Shoe repair firm Timpson, camera company Jessops, and Virgin Holidays and Thomas Cook travel agents all operate Sainsbury's concessions.
In November, Sainsbury's reined back plans for new shops, saying that like-for-like sales had fallen in the half-year.
Retailer Argos is to open ten pilot digital stores in Sainsbury's that will aim to offer a broad range of general merchandise.