"However cloud will thicken with rain developing in Atlantic coastal counties during the morning in strong southerly winds", the weather services said.
Met Éireann says the weather will worsen dramatically after a dry and bright start in most places at first on Monday.
A yellow rainfall warning has been issued for counties Galway, Mayo, Clare, Sligo, Cork, Kerry, Tipperary and Waterford.
"The rain and strong winds will spread eastwards to most places during the afternoon turning persistent and heavy". Met Éireann forecast that he rain will give way to scattered showers during the afternoon and bright or sunny spells will develop. It will be somewhat cloudier in the west with a risk of some rain for a time. Met Eireann is warning that south to southeast winds will reach mean speeds between 50 and 65km/h with gusts between 80 and 110km/h. Showers and sunny spells are on the cards and the heavy winds are expected to decrease later in the day.
Both warnings are valid from 9am this morning and will last until tomorrow.
Temperatures will range from 11º to 13º, as southerly winds become strong and gusty everywhere during the day - with gales on exposed west and south coasts.
Otherwise Tuesday will be a mild day with highest temperatures of between 13 and 16C degrees.
But there is some good news, as the weather is set to finally turn towards the end of the week as temperatures are set to soar as high as 18C on Thursday.
Highest temperatures of between 11 and 13C degrees are predicted.