Winds of up to 130km are expected in coastal ares along with heavy rain and a risk of flooding.
The yellow warning runs from 05:00 BST on Friday until midnight on Saturday and the amber warning from 06:00 on Friday until 18:00 on Saturday.
The public have also been warned to take care near to the coast, with tides at their peak and large waves expected.
The Met Office is warning that there exists the potential for injuries and danger to life, the possibility of damage to buildings and disruption to travel.More news: Korean president to meet Pope with message from N. Korea
Strong winds associated with Storm Callum, coinciding with high spring tides, will hit Ireland on Thursday night and Friday morning, with coastal areas the worst affected.
THE Met Office has upgraded its severe weather warning for tomorrow with torrential rain and gale-force winds set to batter the Cardigan area. Quite widely 40 - 80mm rainfall is possible, but locally 160mm could fall on the highest ground.
"It's also important to remember when driving on exposed roads, such as a motorway, that your own vehicle could be re-directed by a sudden gust so you must make sure your focus is on the task of driving at all times". Fallen leaves will lead to blocked drains and flooding issues.
The national forecaster has issued the Status Orange wind warning for Donegal, Galway, Mayo, Sligo, Clare, Kerry, Dublin, Louth, Wexford, Wicklow, Meath, Cork and Waterford from 10pm Thursday to 9am Friday.More news: CW's Batwoman Reveals First Look At Ruby Rose In Costume
"Certainly, we will have some localised flooding in the east, but the biggest problems will be in the south and west", Ms Cusack continued.
"Widespread flooding from surface water and rivers is possible across south Wales on Friday and Saturday, and is possible but not now expected elsewhere in Wales and parts of north-west England".
The RSA said that with the risk of coastal flooding, motorists should not attempt to drive through flooded areas.
Winds of up to 60 miles per hour are also expected to hit Pembrokeshire, which combined with high tides could lead to some coastal impact due to large waves.More news: Nick Saban Had An Absurd Quote After Alabama’s Win
Gary White, NRW's Duty Tactical Manager, said: "The current forecasted rain could cause flooding this week, especially in south and west Wales, and we are urging people to prepare themselves".