Power was restored to 372 customers on Inis Meáin and Inis Oírr at about 9pm on Monday evening, according to ESB networks.
Residents were without power over the weekend.
The power cut on the Aran Islands meant that the doctor on Inis Oírr had to charge his telephone on a generator in a bar to ensure he could receive emergency calls, a local businessman said.
Inis Oírr businessman Enda Connelly told RTÉ's Morning Ireland that the biggest problem was that the landline service had failed. "As an emergency first aid system it failed.
“Most islands around the world have a stand by generator, we should too.”
Mr Conneely said there would be repercussions for businesses on the islands which have been without power since early on Friday morning after a fault with an undersea cable.
ESB spokeswoman Bernadine Maloney told the same programme that a specialist generator had already been brought to Inis Oírr, but that a transformer was needed to operate the generator. There was no transformer available on the island of Ireland and it had to be brought from the UK.
Bad weather prevented its delivery and it is hoped to ship the transformer from Rossaveal on Monday with a view to having power restored this evening.
Mr Conneely told how islanders had queued to have their mobile phones charged by a generator in a pub. “The doctor had to get his phone charged there too. He had to have a phone so he could take any emergency calls. The doctor’s issue should have been foreseen.”
He said the weekend should have been one of the busiest of the year. “There will be repercussions for business. We have had no phones and no internet. There was no way to respond to bookings or enquiries and if people don’t get a response they go elsewhere.”
Businesses will face losses, he said. The island’s co-op will have to bring in a special skip to remove spoiled food. “Everyone on the island has a deep freezer. There is a lot of spoiled food.
“Business is business and we will recover in some way. But the doctor’s issue needs to be addressed.”
Ms Maloney said that if generators were provided for each island there was no guarantee they would work well if not used on a regular basis because of rust.
“The undersea cable has been there for 20 years. This is the first time there has been a problem.”