Social media sites including Facebook and YouTube were blocked to allow essential services to continue.
"We woke up to pretty good news this morning," Tonga government spokesman Lopeti Senituli told Radio New Zealand.
"It's been two quiet weeks, so people are catching up on the gossip and the what-have-yous."
Chamber of Commerce president Paula Taumoepeau said businesses were hit hard by the blackout while banks were unable to process money transfers for families who rely on income from relatives working overseas.
Tonga was plunged into virtual darkness two weeks ago when the fiber-optic cable was severed. Initially people lost access to the internet almost entirely and couldn't even make international phone calls.
Limited access was restored via satellite, but authorities blocked most people from using social media like Facebook to preserve precious bandwidth.
Residents and businesspeople said they've had difficulty doing anything from reading emails to processing credit card payments.
Piveni Piukala, a director of Tonga Cable Ltd. which operates the cable, told The Associated Press last week that it believes a large ship cut the cable in several places by dragging an anchor along the seabed. He said a domestic cable that connects the main island with some of Tonga's outer islands was cut at the same time.
He said experts on a specialised ship are splicing the cable back together and hope to be finished by Friday afternoon, at which point they can run tests and, barring complications, fully restore the internet over the weekend.
Piukala said it had identified an oil tanker that was in the area when the cable was cut and would work with port authorities and police to determine whether there had been an act of negligence.
He said the repairs are estimated to cost over US$1 million ($1.4m), money the company, which has the government as its major shareholder, can ill afford.
Piukala said he hopes Tonga and other island nations might get together to share the costs of a joint backup plan in the future.
"We don't need a rocket scientist to tell us we need a better plan," he said. "It's a question of funding. The cost of a backup is huge, and for a country like Tonga, we don't have the luxury of money to put aside for a disaster like this. Other priorities are more urgent."
