Officials had warned the storm was set to be one of the most dangerous they have faced and the Irish weather agency, Met Eireann, said a gust of 182 km/h overnight at Mace Head in County Galway provisionally broke an 80-year-old record.
Streets in Dublin were deserted during the usual morning rush hour, as stores kept their shutters down and people heeded a warning to stay indoors until a red wind warning - the highest alert level - was lifted for most of Ireland from late morning.
Irish officials said the storm was set to be one of the most dangerous they have faced. (AP PHOTO)
It was the first time a red warning had been put in place for the entire country since Storm Ophelia in 2017, which killed three people.
ESB Networks, which provides energy for the whole of Ireland, said "unprecedented" damage to its network had led to power outages affecting 715,000 homes, farms and businesses. It expected more power cuts as the storm tracks northwards.
A further 93,000 properties were without power in Northern Ireland.
A spokesperson for ESB said it would take at least a week to restore power for some customers.
Eowyn is the fourth storm in the past four months to knock out power in parts of Ireland. Climate scientists say the link between climate change and the frequency and intensity of violent storms such as Eowyn is still unclear.
Research shows sea levels are set to rise by at least one metre around Ireland this century. Met Eireann warned on Friday of the knock-on risk of coastal flooding.
All schools in Ireland and Northern Ireland were closed on Friday and public transport will not run in Ireland while the red warning remains in place. Non-urgent hospital procedures were also cancelled.
Around 230 flights scheduled to depart from and arrive into Dublin Airport were cancelled, the airport said, adding that further cancellations and delays were possible. Dozens of flights to and from airports at Belfast, Edinburgh and Glasgow were also cancelled.
A red warning is in place for British-run Northern Ireland and Scotland until later in the day.