Eight counties have been placed on a Status Orange wind warning by Met Éireann while Waterford, Cork and Kerry will also be on a Status Orange alert for rain.
Carlow, Kilkenny, Wexford, Wicklow, Cork, Kerry, Tipperary and Waterford have been warned of very strong and gusty southerly winds with some severe and damaging gusts between 9am and 5pm.
Waterford, Cork and Kerry could also see spells of heavy and occasionally intense rain between 9am and 3pm.
A Status Yellow wind warning has also been issued for Leinster, Munster and Galway along with a separate Status Yellow rain warning for Carlow, Dublin, Kilkenny, Wexford and Wicklow.
Both come into effect at 7am and will be valid until midnight.
Disruption is likely in places as Storm Agnes tracks northwards over Ireland, with Met Éireann saying it will be very windy with outbreaks of heavy rain, resulting in possible spot flooding.
Earlier, the forecaster said there would be heavy rain and strong winds, but it will "not be an apocalyptic storm".
It said conditions are likely to result in difficult travel conditions, power outages, fallen trees, coastal flooding and poor visibility.
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Senior meteorologist with Met Éireann Gerry Murphy said there is a possibility of some low level coastal flooding but that the maximum wind and rain expected with Storm Agnes should not correspond with the highest tides.
Speaking on RTÉ's Morning Ireland, Mr Murphy said the storm is still "well in the Atlantic" but its effects will be felt from later this evening when rainfall should begin.
"So overnight, we're going to see the rainfall pushing up across the country and that won't reach the northeast by morning but it'll reach much of the country by morning. And that'll be the first thing to get from Agnes."
It currently looks like the storm will mainly travel up over the southern part of the country, he explained, but that will still bring strong south to southeast winds especially to southern and eastern coastal counties.
However, it is going to be wet and windy everywhere, he said.
There is also a Status Orange marine warning for coastal areas of the east and south.
Met Éireann said that winds will reach storm force 10 at times from Belfast Lough to Carnsore Point to Valentia and on the Irish Sea.
#StormAgnes has been named by the UK Met office for Wednesday. It is the first named storm of the season.— Met Éireann (@MetEireann) September 25, 2023
At the moment we have yellow wind & rain warnings in place.🍃🌧️
Please keep an eye on ➡️https://t.co/juduxcKda8⚠️ for any updates pic.twitter.com/bx5QovEm2W
Mr Murphy said he believes the cyclone centre in Miami overstated the dangers of Storm Agnes when it tweeted that a danger to life could occur during the storm.
"This is certainly a storm depression and will certainly bring stormy conditions off the south coast and off the east coast and if the low pressure tracks further north, certainly the winds will be stronger overland as well in Munster and Leinster - in which case the warnings will increase to orange, but over land, over Ireland, it is high yellow, low orange, it is not an apocalyptic storm."
A Status Yellow wind warning has also been issued for Northern Ireland.
It will be in place from 12pm until 7am on Thursday.
Agnes has been named by the UK Met Office and is the first named storm of the season.
The system will bring strong winds and heavy rain to the UK throughout the day.
"There is a small chance of injuries and danger to life from flying debris," according to the forecaster.
Met Office spokesperson Stephen Dixon said that Northern Ireland "could see in excess of 30mm of rainfall in a relatively short period of time".