Storm Hector hit the northern half of the UK in the early hours, affecting Northern Ireland, Scotland and parts of Ireland and northern England.
The Met Office said winds hit the 100mph mark at the exposed Cairngorms in Scotland, while a gust of 74mph was recorded in Orlock Head in Northern Ireland.
In Edinburgh, emergency services were called to Dalry Road after a woman in her 40s was hit by a roof slate.
North of the Irish border, 23,000 people suffered a disrupted electricity supply and there have been more than 300 incidents of weather-related damage to the network.
Northern Ireland Electricity said 19,000 customers had their power restored by midday, with 4,000 remaining without.
Edel Creery, from NIE, said: “The damage caused by Storm Hector includes power lines brought down by falling trees and poles broken by the high winds.”
In the Republic, 35,000 homes, farms and businesses were left without power.
The worst affected counties were Galway, Mayo, Sligo and Donegal, but Ireland’s electric board ESB said teams were working to restore power.
Trees have fallen in the winds, causing travel chaos throughout Scotland, where “chainsaw gangs” have been deployed by ScotRail to remove branches from the lines.
Police had to close the Tees flyover to high-sided vehicles and the Shields Ferry across the Tyne was not operating.
The Tay Bridge was closed to all traffic, while the Forth Road Bridge was closed to double decker buses.
There has been heavy rainfall in Cumbria, with 3.2in (80mm), and 5.1in (130mm) in the Isle of Skye in the last 24 hours.
Storm Hector is now due to pass out into the North Sea, and will be followed by a much weaker weather front.
A Met Office spokesman said: “By Thursday evening the low pressure system which brought the strong winds will be moving out towards the North Sea.”
While there could be thunder in some places on Saturday, there is likely to be some sun this weekend, with Sunday looking drier.
Met Office meteorologist Aidan McGivern said: “The wettest weather will be out of the way but there will be some blustery showers following and with the yellow warning in force disruption is possible.
“Further spells of rain will push their way into Scotland through the night before clearer skies open out by the start of Friday.”
However, the winds have boosted Britain’s wind power network, with 34.5% of the country’s electricity coming from wind between 9.30am and 10am on Thursday.
On calmer days, the country usually takes about 6% of its power from wind.