Police Scotland's head of road policing Hilary Sloan said it was "very important" people do not travel, with driving conditions likely to be treacherous and severe disruption to public transport.
Train company Avanti West Coast - which runs cross-border trains - warned that passengers should not travel north of Preston, while Transpenine Express said it was "urging" customers not to travel to Scotland and LNER advised travellers to avoid going north of York.
On social media rail operator ScotRail said it was "working with industry partners" to determine what action to take.
A number of bridges, including the Forth Road Bridge, will implement speed restrictions.
Flood gates at Broughty Ferry and Riverside in Dundee will be closed later due to the expected conditions.
The Royal National Lifeboat Institution urged people living near the coast to "stay vigilant" in the conditions.
Michael Avril, the organisation's water safety lead for Scotland, said: "If you plan to visit the coast, the RNLI advises that you stay a safe distance from the water as conditions could knock you off your feet or wash you into the sea.
"It is not worth risking your life."
Glasgow Warriors rugby team had already moved their Friday night fixture with Connacht to Sunday as a result of the warnings, while Caledonia Gladiators basketball team postponed their fixture against Leicester Riders.
Entertainment venues such as the Glasgow Science Centre and the Glasgow Film Theatre announced they would be closed on Friday, though the latter said it hoped to open at 18:00.