Properties in the Highlands, Tayside, Argyll and Dumfries and Galloway were worst affected as winds of up to 142mph battered the country on Thursday.
Scottish Hydro said more than 80,000 customers lost power as electricity lines and conductors were damaged.
Around 70,000 of those affected were back on the grid within a day and the last of the homes cut off have now been reconnected.
Scottish Power faced similar problems with 50,000 customers losing power but they have now repaired the supply.
It is estimated there were 300 high voltage faults, around 800 breaks in conductors and a large number of wooden poles holding power lines needed to be replaced, some in remote areas.
Thousands of engineers worked to fix the problems and "welfare vans" were sent to affected areas to provide hot water, food and drinks.
Scottish Hydro's head of engineering Alan Broadbent said 1100 engineers and support staff had worked to restore power.
He said: "Scottish Hydro Electric Power Distribution provided hot food and drinks through local cafes and restaurants and mobile catering units. Mobile generators were also connected to care homes and other priority locations.
"Although power has now been restored, our work is not yet complete. We will still have a presence in some areas over the next few days to carry out further repairs and follow-up work."