While not admitting legal liability, the commonwealth settled a class action the day a Federal Court trial over the saga had been due to start.
The government agreed on Monday to pay $112 million in compensation to about 400,000 individuals as well as legal costs.
It also dropped $398 million in debts it had been pursing against class action members.
This comes on top of $720 million in refunds announced in May over the faulty income assessments.
This involved matching Australian Taxation Office and Centrelink data to claw back welfare benefits the government said were overpaid.
But the scheme was last year ruled unlawful, with the Federal Court saying Centrelink could not have been satisfied the debt was correct.
Income averaging is no longer used as the sole proof for a possible debt.
Following Monday's settlement, Government Services Minister Stuart Robert said $705 million had already been repaid to 405,000 Australians.
He also said this represented 95 per cent of those who had their debts raised using the government's discredited income averaging method.
Further compensation would cover interest earned on money collected by the government, the minister added.
Gordon Legal partner Andrew Grech labelled the settlement a fair and reasonable outcome.
"No money amount will ever compensate people for the hardship they've been through. Many people have been in really difficult circumstances," he said.
We've listened intently over a long period of time now to the more than 70,000 people that have contacted us and there are some really dreadful stories you hear through that process.
Federal Labor frontbencher Bill Shorten is continuing to push for a robodebt royal commission.
"We said it was illegal and the government ignored us. We said it was unfair, the government ignored us. We asked for documents in parliament from the government and they ignored us," he said.
"Why should people have to go to lawyers, put together a class action just to get the government to obey the law?"
The Australian Council of Social Service also called for an independent and arms-length inquiry into "this extraordinary abuse of government power".
"We all need an assurance that a terrible scheme like robodebt can never be repeated. We also need people responsible to be held to account in an open and transparent manner," ACOSS chief executive Cassandra Goldie said.
The final detail of the class settlement requires approval by a judge and the case will return to court at a later date.
Gordon Legal said it hoped to finish distributing the repayments by the end of next year.