A £700 cap on compensation has also been lifted, allowing those affected to claim £70 for each 12-hour period they are left without power, after an initial £70 for the first 48 hours.
The Army has been deployed to help residents in Scotland and England who have been off supply for a week since the storm on Friday November 26 caused "catastrophic damage" to the electricity network.
The Energy Networks Association said 9,200 people are still without power, down from 15,000 on Thursday evening, of which 6,650 are in the North East, 1,300 are in the North West and 1,250 are in Scotland.
Ofgem has said its review will establish the facts about the response and if necessary it will pursue further enforcement action.
Jonathan Brearley, Ofgem's chief executive, said: "We understand this is a really worrying time for people who are without heat and power as the severity of Storm Arwen has hit homes and businesses in the North of England and Scotland. The effects of Storm Arwen are still being felt with 10,500 homes still without power.
"We accept the network companies have been working in challenging conditions, but until every home in Britain has power restored, that relentless effort must continue.
"We are launching a review into how the storm has been handled. We have strict rules on how network companies need to operate in these circumstances and we will take action if needed."
He added: "I've launched an urgent review to see if there are things that the industry could learn from this response in order to improve our support to consumers in the future."
The review will focus on the role of the network companies in maintaining the resilience of the system and their emergency response, including their communications with customers.
Around 130 troops have been sent to carry out door-to-door checks and offer welfare support in north-east of Scotland, where around 1,600 Scottish and Southern Electricity Networks (SSEN) customers remained off supply at 10am on Friday.
Helen Shand, who lives in Inchmarlo, Aberdeenshire, was left without electricity, and made the decision to go to her son's house in a nearby village after a few days because of the outage.
She said: "It was miserable. I have never been so cold in all my life, even the dog was cold."
SSEN said it expects to restore power to 1,100 homes throughout the course of Friday and into the evening and around 500 customers are expected to be reconnected throughout the course of Saturday.
A spokesperson for SSEN Distribution said: "We welcome Ofgem's decision to conduct a review into Storm Arwen, particularly given the significant impact on our customers and on our network.
"We look forward to capturing any lessons learned, alongside the outcomes from our own review process.
"In addition, we were pleased to agree with Ofgem the removal of the cap on compensation that can be issued to customers affected.
"This is a welcome first step and commensurate with the exceptional nature of this weather event.
"We will also explore further enhanced levels of support for our customers and communities once all customer supplies are restored."