Northern Ireland Electricity (NIE) said the extreme weather had caused hundreds of faults across the region, particularly in Northern parts and some people could be in the dark overnight.
Gusts of 60-70mph were recorded between 5am and 7am on Tuesday, and the severe winds and fallen trees have brought down power lines.
The Met Office issued an amber warning urging people to be prepared for disruption due to strong winds. The alert ended at 6pm on Tuesday.
NIE said repair work will continue on Wednesday in the Ballymena, Ballyclare, Campsie and Bangor areas, which were among the worst hit.
Sara McClintock, NIE Communications Manager said: "We succeeded in restoring power to tens of thousands of customers within the first 12 hours thanks to the tremendous effort of all staff, from engineers and linesmen to logistics and call handling.
"We are concentrating now on restoring power to customers who have experienced the very worst damage caused by this storm."
The windiest conditions were observed throughout the morning across parts of the North Coast and Down Coast, with winds of over 80mph recorded ahead of rush hour, and gusts of up to 105mph in Malin Head in Co Donegal.
A pensioner told UTV she was shaken after a large tree fell in her garden on Broomhill Avenue in Londonderry shortly before 6am.
"Another couple of inches, it would have been through the window," Audrey Douglas said.
"I heard this unearthly noise; it was so loud it was unbelievable," she said.
"I looked out the front door and the tree from the house across the street was in my front garden... The house next door, their car was on the driveway of their home - it was just flattened, badly damaged."
Met Office spokesman John Wylie says the worst in now over in Northern Ireland.
"It was only a two hour blow of very strong winds, certainly enough to bring down lots of trees and some power cable as well," he said.
The adverse weather conditions disrupted traffic across the region, as many roads were closed because of fallen trees.
Police warned motorists to take care when driving and slow down, while the Roads Service said the public should exercise care when travelling and expect debris on roads.
Areas affected included Londonderry, Coleraine, Larne, Omagh, Belfast, Downpatrick and Newry.
In Enniskillen, the storm force gales were so powerful that a large section of the roof at the town's ASDA store was blown off.
While the wind is expected to ease on Tuesday evening, a yellow warning of rain has been issued for Wednesday, when the Met Office said the public should be prepared for wet and windy weather.
The forecaster warns that heavy rain and strong winds could lead to localised flooding in western areas.
The following roads have been reported as being closed (*):
Bishop St, Londonderry, closed due to an unsafe building.
C557 Hillhead Rd Castledawson remains closed due to a fallen tree.
The C647 Carricklongfield Road, between Aughnacloy and Dungannon, is closed to traffic due to a fallen tree between Carricklongfield Road and Legane Road. This road will remain closed until Wednesday 4 January. Diversions have been signed.
(*Source: Roads Service)