Bob Hallam and Stuart Andrews were joint winners of the naming competition organised by Stroud Town Council.
The competition, which was supported by Stroud Life and the Cotswold Canals Trust received 65 entries.
The town council decided to run the contest after it awarded a £15,000 grant to the Cotswold Canals Trust to buy the two mud barges.
They will be used for canal maintenance and will be officially launched in a ceremony by Mr Hallam and Mr Andrews later this year.
Mr Andrews, who was a volunteer on the canal for several years, is so thrilled about his win that he plans to travel to Stroud from his home in Southern Spain for the big event.
The judges – Stroud Life Editor Ben Falconer, Mayor Kevin Cranston and Val Kirby, vice chair of the Cotswold Canals Trust – were looking for names that were linked together and expressed the spirit of Stroud.
Mayor Kevin Cranston said Warp and Weft were the natural winners.
“Warp is the long thread in a roll of cloth and the Weft is the shorter thread that crosses the warp. We chose the names as they clearly show a link with Stroud’s historic mills and weaving industry,” he said.
“A warp is also a name for a rope used for mooring boats. We also thought that the canal was like the Warp threading is way through the length of the valley whilst Weft represents the links reaching out to and drawing in the community from the sides of the canal.”
The judges praised the Year 10 CoPE (Certificate of Personal Effectiveness) students at Thomas Keble.
“I was particularly impressed by the entries from Thomas Keble School, which had made a great effort to research the history of the canal and the people who built it,” said Stroud Life editor Ben Falconer.
“I hope to see Warp and Weft plying the canal for many years to come.”