The Euklisia rug, patented by Newtown entrepreneur Pryce Jones in 1876, was exported around the world in the late 19th century.
Documents at Powys archives in Llandrindod Wells show Pryce Jones sold 60,000 rugs to the Russian army. BBC Wales researchers have also found records of the rug in the Australian Outback, and at missionary posts in the Congo.
However, inspite of the large number of rugs that were distributed worldwide, programme makers could not find a single example of the rug existing today. Undeterred, they decided to recreate the rug using the original patent.
The rug was recreated by Jane Beck, an antique cloth specialist from Tregaron in Ceredigion. She said it was a simple design - but would have been a welcome piece of equipment for soldiers who used it.
"It looks very primitive now but I am sure the soldiers were very glad of it at the time," Jane said.
The rug, made from Welsh wool, has been donated to Newtown Textile Museum, which already boasts displays of Pryce Jones artefacts, and will go on display when the Museum reopens in May.
Eddie Butler said, "It was great to see this Welsh first brought back to life.
"It didn't look anything like a sleeping bag today - it's more of a folded rug. But you can see it only needed a couple of fasteners to be more recognisable as a sleeping bag.
"However simple it is, it must have been a great bonus for troops - especially in places like Russia. I expect this Welsh invention helped thousands of soldiers to get a better night's sleep."
Wales and the History of the World, Wednesday 10 March, 7.30pm, BBC One Wales.