Northern Powergrid announced last night that all of its customers had been reconnected and said it has sent engineers to help restore supplies in other parts of the country.
The storm caused what providers believe was a record national outage over a 24-hour period on Friday, with around 1.4m homes affected.
Around 83,000 people were still without power this morning, according to the Energy Networks Association, and the Met Office has warned that Storm Franklin may cause further disruption over the next 24 hours.
In a statement, Northern Powergrid said: “We are pleased to confirm that our teams have reconnected all customers affected by Storm Eunice.
“We are grateful to the fantastic team of people who have worked to restore supplies to over 30,000 customers and to support all those affected.
“We are grateful to our customers for their patience as we worked to restore supplies and apologise for the inconvenience caused by the disruption, particularly to those who had to wait the longest.
“Whilst we’re pleased all customers affected in our region have been restored, we know that the storm has done much more damage further south.
“So far, we have been able to release resources into the industry mutual aid arrangements to support the efforts of those companies who helped us recently when our region took the brunt of the damage. We are hopeful of being able to do more as the weekend progresses.”
Storm Franklin is expected to cause further disruption and the Met Office has issued a yellow weather warning for wind, which will be in place in Yorkshire until 1pm tomorrow.
The forecaster has told people to expect “very strong winds” and said “power cuts may occur”.
It is the first time the national forecaster has recorded three major storms in such quick succession since the naming system was introduced seven years ago.
Last year, Northern Powergrid was heavily criticised when hundreds of customers were left without power for 11 days after Storm Arwen.
The storm caused widespread disruption in November and around 240,000 homes lost power.
Earlier this week, the company apologised to 74 of their customers after homes were accidentally issued Storm Arwen compensation cheques of more than £2.3 trillion.