Met Éireann predicted counties such as Dublin, Carlow, Kildare, Laois, Longford, Louth, Wicklow, Offaly, Westmeath, Meath, South Galway, Clare, Limerick and Tipperary would be especially affected by the storm, which has been named Eleanor.
Police and council workers are blocking streets, diverting traffic and handing out sandbags, people in the area have said.
"There is a small chance of injuries and danger to life, as well as minor property damage, from flying debris", it said.
The Met Office warning lasts until 04:00 GMT on Wednesday.
A status yellow wind warning is in place for Donegal as Storm Eleanor hits Ireland.
Gales, with gusts of 60mph to 70mph, are likely.
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Residents in coastal areas have been warned of possible 80mph gusts as Storm Eleanor approaches.
Coastal roads and properties along Britain's western and southern coasts are vulnerable to high waves throwing beach material on to sea fronts, forecasters warned.
In addition to this they are also forecasting for a band of rain to pass through Cumbria this evening and into Wednesday morning, which has the potential for some river levels to reach Flood Alert thresholds.
Carol Halt, the agency's flood duty manager, said: "We urge people to stay safe on the coast - take extreme care on coastal paths and promenades, and don't put yourself in unnecessary danger trying to take "storm selfies".
However, late afternoon, weather officials issued a second amber wind warning.
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