Shoppers at the 125 stores in East Anglia will be able to pick up the "perfectly edible" items from Monday as part of a campaign by the chain to reduce its impact on the environment.
Tinned goods and dried food which carry "best before" dates, rather than "use by" dates, will be included in the scheme.
According to the Food Standards Agency, the "best before" date is about quality, not safety, and food is safe to eat after this date but may be past its prime.
Roger Grosvenor, joint chief executive of East of England Co-op, said: "This is not a money-making exercise, but a sensible move to reduce food waste and keep edible food in the food chain.
"By selling perfectly edible food we can save 50,000 plus items every year that would otherwise have gone to waste.
"The vast majority of customers understand they are fine to eat."
The Food Standards Agency estimates the UK throws away millions of tonnes of food every year, the majority of which could have been eaten.
The East of England Co-op's campaign, entitled The Co-op Guide to Dating, will run with the slogan "Don't be a binner. Have it for dinner!"
Welcoming the move, Paul Cook said: "It's really good news. A third of all food produced in the world goes to waste and there is a huge amount of carbon and greenhouse gas emissions that goes into producing and transporting that food.
"We seeing the impact of a changing climate as a result of those emissions on the very poorest people."
Describing it as a "Christian duty" to clamp down on waste, he said we can all do something to help.
"Making small changes in our lifestyle can add up to a big impact for those in poverty."
(additional reporting by the Press Association)