The Bureau of Meteorology said at about 5am (AEST) that north-westerly winds of 50 to 60 kilometres an hour would develop in the west early this morning before moving eastward.
Damaging gusts of about 110km/hr are expected.
Dangerous winds averaging 60km/hr to 70km/hr, peaking at about 100km/hr, are also expected to develop around King Island.
They will extend eastwards to the north-east coast and the Furneaux Islands by this afternoon.
In the capital Hobart, damaging gusts are expected from late morning into mid-afternoon.
The Bureau said winds are expected to ease below warning thresholds throughout the state by this evening.
The current warning covers all 11 weather districts in the state.