A Met Office spokesman said: "As Storm Callum passes to the northwest of the United Kingdom, a period of heavy rain will affect South Wales during Friday, with further spells of persistent and heavy rain at times during Saturday".
The Met Office issued an amber warning for heavy rain in south Wales until 18:00 BST on Saturday.
The Republic of Ireland has been the worst affected by Storm Callum, with 20,000 homes and business left without power on Friday morning.
Ferry services between Wales and Northern Ireland and Dublin have been suspended.
The weather warning is due to stay in force until midnight.
Power cuts could also result and other services - including mobile phone and broadband network coverage - could be impacted.
In Galway city, coastal routes along the harbour are closed as a precaution ahead of high tide at around 7.45am.
"We also have yellow and amber warnings of between 50mm and 150mm of rain for Wales. Some roads and bridges may close".
Met Éireann said the strong winds will continue for the morning, with the Status Orange warnings for Storm Callum remaining in place until 5pm for northwestern coastal areas.
Rainfall totals could reach as high as 150mm over the Brecon Beacons, almost as high as the monthly average of 170mm for Wales.
Chief Meteorologist Frank Saunders, said; "Strong winds at this time of year can increase the rate of leaf fall which can potentially block drains or culverts and, with the heavy rainfall expected over Friday and Saturday, could well heighten the potential for flooding". The low centre may drift further west and the winds will not be as strong.