The storm is expected to bring strong winds and heavy and persistent rain, particularly in western areas.
It is not expected to be as severe as Storm Desmond, which brought gales and heavy rain earlier this month.
In the Republic, Met Éireann has issued a number of weather warnings, valid from lunchtime until Wednesday night due to Storm Eva.
Storm Eva is expected to hit the west and north west of the country, bringing some severe winds to coastal counties.
A Status Orange wind warning applies for Donegal, Galway, Mayo, Sligo and Clare with gusts of up to 75 miles per hour expected between 16:00 and 21:00 local time on Wednesday.
For the counties of Leinster, as well as Cavan, Monaghan, Leitrim, Roscommon, Cork, Kerry and Limerick, a Status Yellow wind warning applies from lunchtime, with gusts of up to 70 miles per hour expected on Wednesday evening and night.