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, "I would like to thank everyone who has been affected by the loss of power for their patience. While the majority of customers had their power restored by the end of the first day, a number of areas sustained significant damage and engineers worked late into the night and from early in the morning to repair the network.
"Scottish Hydro Electric Power Distribution (SHEPD) had over 1,100 engineers and support staff working to restore power and over 130 call centre operators handling customer calls.
"During this time, looking after our customers was a priority and SHEPD 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 to restore the network to normal operations."
A lorry driver died and commuters faced major travel disruption during the severe weather. The entire rail network was shut down and flood warnings were put in place along the east coast as a tidal surge was expected.
Scottish Hydro said all reported incidents have been dealt with, but asked any customers who may still be without power to contact them on 0800 300 999.