Prime Minister Boris Johnson confirmed around 130 troops had been sent to the Grampian region, where 3,000 homes are still dark following damage to power lines over the past week.
Troops will conduct door-to-door checks on more than 4,000 homes, and provide welfare support for remote communities.
Mr Johnson said: “It was a very, very big storm. We are doing everything we can to to help people.”
The Department for Business, Energy and Industrial Strategy (BEIS) said almost a million households have been affected by power cuts over the past week, but electricity has been restored to 960,000 homes.
Scottish and Southern Electricity Networks (SSEN), which distributes power to 3.7 million homes in the north of Scotland and central southern England, said the worst-affected areas include Aberdeen, Aberdeenshire, Moray, Angus, Perthshire and Stirlingshire.
The firm said as of noon on Thursday, 3,100 customers remain off supply in Scotland, while more than 125,000 have had power restored.
Aberdeenshire is the main area affected, with 2,400 customers waiting to be reconnected there and in Aberdeen.
There are also around 300 still without power in Angus, around 200 each in Moray and Perthshire and some 25 in Stirlingshire.
SSEN said it aims to restore power to the vast majority of homes still affected by Friday, subject to no new damage being identified or unforeseen challenges.
But the firm said “small pockets of customers on SSEN’s low voltage network in Aberdeenshire will not be reconnected until Saturday”.
The company plans to contact these customers to offer support, including accommodation.
Aberdeenshire Council said: said on Twitter the military support would supplement the actions of the council and praised those offering community assistance.
The council added: “Rest assured we continue to work tirelessly to provide the support our communities need at this challenging time.”
Mark Rough, SSEN operations director, said: “As Aberdeenshire is the main area which continues to be impacted by Storm Arwen, when power is restored to customers in other regions we are redeploying additional resources to support restoration efforts, as well as enhancing welfare provisions in the region.
“Due to the extent of damage on the low voltage network, particularly to single premises, some customers in Aberdeenshire will regrettably remain off supply until Saturday and our teams will proactively contact those customers to offer whatever support is required.”
Meanwhile, the National Trust for Scotland has said the weather has had a “devastating” impact on wildlife and trees.
About 800 seal pups are feared to have died at its Berwickshire site as a result of the storm.
At Castle Fraser, about 200 trees are down and the Pittendreigh wood at Leith Hall has been badly damaged, with estate trails at Crathes Castle, Haddo House and Brodie Castle also blocked.
People are asked to stay away from the properties until they are made safe.
In the south-west, Culzean Country Park and Threave Estate also lost trees, causing some damage to buildings, including the 19th-century pagoda at Culzean.
At the Mar Lodge Estate National Nature Reserve a project to repair its historic Victorian bridge has been set back.