It has warned this could cause severe flooding and damage to property in the affected areas, as well as difficult driving conditions.
Met Éireann’s red warnings – its highest level of alert – are in force until 10:00 local time on Saturday.
It has also issued a status orange warning for rain in counties Waterford, Kerry, Clare, Mayo, Sligo and Leitrim over the same time period.
In County Donegal a status yellow warning is in force for snow/ice, rain and strong wind until noon.
That county has been the worst hit for power cuts, with about 12,000 people without electricity, particularly in the Gweedore and Buncrana areas.
Other counties affected include Kerry, Sligo, Leitrim, Roscommon and Galway.
The naming of storms is a practice which helps meteorologists communicate with the public when they need to advise of dangerous or disruptive weather events.
Certain criteria have to be met before a storm is given a name.
Bert is the second named storm of the 2024/25 season which began on 1 September.
It was named by Ireland’s Met Éireann on Thursday because Irish forecasters believed it could bring severe disruption to the Republic of Ireland.
Met Éireann works in partnership with the UK Met Office and the Royal Netherlands Meteorological Institute (RNMI) every year to monitor, classify and names storms.
The three organisations agree an alphabetical list in advance of each season.
Storm Bert was preceded by disruptive snow in some parts of Northern Ireland on Friday.
Some Translink services did not run on Friday morning, including buses serving Belfast, Ballygowan, Derryboy, Omagh and Newcastle.
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