The move is part of a commitment by the business to lower prices, which has featured the retailer benchmarking its prices against Asda instead of Tesco.
The retailer, which launched Brand Match three years ago, had previously benchmarked its prices against Tesco through the scheme, but will now match brand prices against cheaper rival Asda in a bid to reposition the value credentials of the brand.
It said it would match the prices of Asda brands, "even when they’re on promotion", from 2 October.
Sainsbury’s said the move, part of a major pricing drive, would make its proposition "straightforward and easy to understand". It would also slash the cost of "thousands" of lines across the food business, ditch "confusing price mechanics" and introduce "round pound" pricing across more products.
"For customers this means that they can buy what they like, when they like because the regular price of those products will be affordable everyday rather than just when that product is on promotion," the retailer said.
Sarah Warby, Sainsbury’s marketing director, said: "Customers tell us they find supermarket prices and promotions confusing and don’t always know who to trust when it comes to getting good value.
"So we’ve taken this feedback on board and we're making it easier for customers to buy the products they love, whenever they like, safe in the knowledge that they can get good value all the time on all products, without having to wait for promotions.
"We will continue to run as many promotions as before and they will be just as competitive, but customers now have the added reassurance that prices will always be great value at Sainsbury’s, both on and off promotion."