Speaking at a meeting of the full council this week, she praised the men’s and women’s teams for their “dedication to excellence” and for “putting Dumfries and Galloway on the world curling map”.
Three of the silver medal-winning male team come from Dumfries and Galloway while Vicky Wright from Stranraer won gold with the ladies’ team.
The success comes as Dumfries Ice Bowl plays host to the Scottish Curling Championships for the first time.
Councillor Murray said: “I would like to congratulate both teams on their historic achievements.
"The hard work and dedication to excellence that goes into achieving such success is an inspiration not only to everyone living in Dumfries and Galloway, but also across Scotland and the UK.
“We are blessed in Dumfries and Galloway with having excellent curling facilities in Lockerbie, Stranraer and Dumfries Ice Bowl.
“Such facilities, an active schools programme in Curling’s Cool and the close partnership working between Dumfries Curling, Scottish Curling, the many clubs throughout the region and the council give us every chance of building on this success in the decades to come.
“And maybe, in 20 years’ time, there’ll be a new generation of athletes with Olympic dreams, inspired by the exploits of Grant Hardie, Hammy McMillan, Bobby Lammie and Vicky Wright.”