Police said no motorists should travel in or to the red weather warning area while train operator ScotRail said all services were being suspended due to safety concerns.
The Met Office red warning runs from 10am to 5pm and covers the central belt including Glasgow and Edinburgh, stretching north on the west coast to Jura in Argyll and Bute and south to Stranraer in Dumfries and Galloway.
Schools and nurseries across Scotland will be closed, except in five council areas, while non-urgent planned procedures have been postponed in NHS Lanarkshire and NHS Lothian.
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Forecasters said the weather conditions bring a “risk of significant disruption to transport and power supplies as well as dangerous conditions outdoors”, with “very dangerous” driving conditions because of fallen trees and other debris.
They also warned of the potential for damage to buildings and homes.
Police Scotland Chief Superintendent Hilary Sloan said: “Our advice to any road user is not travelling, and that’s really the message we want to get across today.
“It’s really unusual for us to have a red weather warning and that advice is in place for the duration of that warning.”
In a statement at the Scottish Parliament, First Minister John Swinney said: “The Met Office advice is clear, the potential impacts include danger to life, structural damage to property and transport and power disruptions.
“We have to be clear, people should not travel.”