A Status Yellow wind warning for counties Carlow, Kildare, Kilkenny, Laois, Longford, Offaly, Westmeath, Cavan, Monaghan, Leitrim, Roscommon, Limerick and Tipperary has also been issued by Met Eireann.
Storm Callum brings with it a risk of flying debris and tiles blowing off of roofs.
By Sunday, the weather is expected to settle down slightly as both warnings are lifted.
Today's unseasonably warm weather will be replaced by the strong winds and heavy rain felt at the beginning of the week as we head into Friday and Saturday.
Spray and flooding is also likely to lead to hard driving conditions and some road closures.
The national forecaster has issued the Status Orange wind warning for Donegal, Galway, Mayo, Sligo, Clare, Kerry, Dublin, Louth, Wexford, Wicklow, Meath, Cork and Waterford from 10pm Thursday to 9am Friday.
Met Office meteorologist Greg Dewhurst said: "Storm Callum is coming from the middle of the Atlantic".More news: Event highlights mental health issues
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Areas of high ground could see over 60 mm of rain in 12 hours with some exposed locations seeing as much as 100 mm by the end of the day.
Winds will be strongest along the coast and there will also be a danger of some coastal flooding due to a spell of heavy rain and high tides.
Richard Brown, Pembrokeshire County Council's Head of Environmental Services and Public Protection, said that although Council staff would be working continuously to clear the roads, motorists would need to be vigilant.
"Storm Callum is the 3rd named storm of the 2018/19 season". The worst of the winds will impact on Friday morning rush hour, people will be travelling in Scotland for October holidays.
"Widespread flooding from surface water and rivers is possible across south Wales on Friday and Saturday, and is possible but not now expected elsewhere in Wales and parts of north-west England".
Natural Resources Wales' (NRW) have said they are sending out their emergency response teams to prepare for the storm, checking that flood defences are in good working order, clearing gulleys and ditches, and installing temporary defences.
"Though the winds will ease down by late morning/forenoon, a sting in the tail will follow, with a deterioration likely again later, as the trailing waving weather front potentially feeds up further pulses of heavy rain from the south, with the possibility of a further core of severe southerly gusts for south, southeast and east coasts towards evening".