The bags began being phased out from April 30, with all remaining stock expected to be sold by the end of this summer.
Instead the retailer is replacing single-use bags with 10p compostable carriers in all stores.
The fee for single-use plastic shopping bags will double to 10p in May in the bid to reduce pollution by plastic in the environment.
The Co-op is also calling for all single-use carrier bags to be certified compostable and to introduce a minimum 50p price for reusable bags.
Data from Greenpeace suggests that supermarkets distributed more than 1.5billion so-called 'bags for life' in 2019, weighing a total of 44,913 tonnes - a 56% increase on the year prior.
During production, 'bags for life' use more plastic than conventional single-use carriers. The Co-op has said its new initiative would remove 29.5million, weighing around 870 tonnes of plastic, from sale each year.
Jo Whitfield, chief executive of Co-op Food, said: "With over 1.5 billion bags sold each year by retailers, this remains a massive issue for our industry as many shoppers are regularly buying so-called ‘bags for life’ to use just once and it’s leading to major hike in the amount of plastic being produced.
“We believe that it should be mandatory for all retailers to report on the sales of all of their reusable bags, not just single-use bags. Right now, Co-op is the only major retailer to report on all of the bags it sells. This policy would enable a fuller understanding on the impact of the levy and its true effect on shopping behaviours when customers are making decisions at the tills.”
Helen Bird, strategic engagement manager at waste and resources body Wrap, said: "The most important thing to reduce this impact is reuse. Just as we all now carry a mask about ourselves, we should be doing the same with shopping bags."
The Co-op was the first retailer to make compostable carrier bags widely available when it rolled them out to over 1,000 stores in 2018. The bags are certified compostable, with a secondary use as a food waste caddy liner in the home, collected as part of Local Authority household food waste collections. The bags are also suitable for use in home-compost bins.