Ch Supt David Robertson said: “Cancelling such an event was a difficult decision for the organisers, but public safety takes priority, so we fully support this decision.”
The Hogmanay celebrations have previously been cancelled due to adverse weather in 2003 and 2006.
The Met Office yellow rain and snow warning extends from central Scotland to the north of the country.
Forecasters said the weather warnings could lead to difficult driving conditions, disruption to public transport, power outages and homes being cut off.
There is also an amber warning in the Highlands, stretching from Inverness to Fort William, from midnight until 17:00 on Tuesday.
Transport Scotland said restrictions on use of some bridges may come into force over the next 24 hours.
Justice Secretary Angela Constance is also due to lead a meeting of the Scottish government’s resilience room later.
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