John Chichester, who runs T-Box Solutions, is supplying the boxes to Tesco Extra stores in Wales and the West Midlands. Asda has also been running a trial of them.
The product, which received a gold medal at the International Invention Show in Geneva, consists of a set of boxes that fit into a shopping trolley so that shoppers can divide their shopping into frozen, fresh and dry goods.
On an average shopping trip, the boxes save two and a half minutes at the till and can save up to 15 plastic bags a shop, Chichester claimed.
"It is the environmentally friendly option to the plastic bag," he said.
"The boxes are made of 100% recycled paper and are very strong. It's a leap of faith for retailers but the benefits are great. They win hands down. It is convincing people to change the way they shop and people like it."
There are two ranges available a four-box version that fits into a large trolley, and a three-box version that slots into a smaller trolley. Prices start at £3.49 and last for about 20 shops.
The new invention is one of a number of measures being rolled out in supermarket chains across the country to cut customer wait times at the till.