The paper bags can hold up to 16kg and Morrisons said they are “reusable, recyclable, water resistant, tear resistant”.
The paper bags will cost 30p and there will be cotton and woven bags available too, costing between 75p and £2.50.
Morrisons has said it will save 3,200 tonnes of plastic per year by scrapping plastic bags from its stores.
Almost 100 million plastic bags will be removed in total.
Morrisons trialled the paper bags in stores last year, and it proved to be successful.
David Potts, Chief Executive at Morrisons, said: “We have been listening hard to our customers over the past year and we know that they are passionate about doing their bit to keep plastics out of the environment.
“Removing all of the plastic bags from our supermarkets is a significant milestone in our sustainability programme.”
One customer commented: “Touching up the meat after touching up containers from people isn’t the one in a pandemic… Good idea but not at the moment really.”
Another shopper said: “Totally unhygienic given what’s going on in the world. Some people are not clean, so although I get the plastic and paper waste, don’t think it’s good people bringing stuff in from home.”
Another customer added: “Like the idea and is good, but in a pandemic possibly increasing contamination this has put me off the counter full stop if this is happening. All precautions should be taken at the minute.”
Furthermore, Morrisons recently pledged to become the first supermarket to be completely supplied by net zero carbon British farms by 2030, hoping to work with 3,000 farmers and growers to produce affordable net zero carbon meat fruit, and vegetables.