But the deal will cost slightly more than originally budgeted, and must be approved by bailout creditors who are lending Athens the necessary funds.
The agency said in a statement it will pay banks, funds and other private bondholders roughly 33.8 per cent of the bonds' face value.
That is still a highly attractive option for some, as the bonds have been trading well below face value since a major debt writedown in March. Investors brave enough to have bought Greek debt just a few months ago now stand to make 200 per cent gains.
The buyback will shave some €20 billion ($26 billion) off Greece's €340 billion ($442 billion) debt, which is now mostly held by its bailout creditors — its European partners and the International Monetary Fund.
The yield on Greek 10-year bonds dropped to about 12.6 per cent Wednesday, its lowest since the March writeoff and a sign of greater investor confidence in the country's ability to manage its debt. The Athens stock index was up 0.5 per cent in afternoon trading.
The government had no immediate comment on the result of the deal, saying it would await a meeting on Thursday of European finance ministers, who must sign off on the buyback.
Under the terms of the buyback, Greece would spend €11.3 billion of its bailout funds on the bonds — more than the €10 billion initially budgeted. The question remains whether bailout creditors will accept the extra outlay.
Jonathan Loynes, chief European economist at Capital Economics, said the required additional cost was unlikely to derail the deal.
"It would be extraordinary if the whole thing fell apart over an amount that small," he said.
He said it was a relief that the deal had been successful because there was a danger that some investors might have held out for better terms.
"They're over that hurdle and that's all good news, but the major challenge is to try to achieve the lasting economic growth that really is going to be needed if the debt ratio is going to come down in the way it's predicted," he said.
Greece is heading for a sixth year of recession. The cumulative drop in economic output is expected to reach 25 per cent — a staggeringly figure that has been compared with the Great Depression of the 1930s.
The successful buyback deal was a major requirement before Greece could be granted a long-delayed installment of its international bailout funds. Athens expects Thursday's meeting to approve payment of the €34.4 billion, most of which is earmarked to shore up the country's struggling banks.
That's why domestic lenders all decided to participate in the buyback, relinquishing the prospect of long-term gains on the bonds, for the certainty of a big capital injection in the next few days.
Early indications were that creditors would approve the deal and release the funds. Simon O'Connor, spokesman for EU monetary affairs commissioner Olli Rehn, wouldn't comment directly on the buyback but said: "We expect that the decision on the disbursement will be taken tomorrow as planned."
IMF chief Christine Lagarde expressed satisfaction with the deal. "For the moment I can only welcome the results that have been produced by the debt buyback," she said before the official results were released.
Athens has depended on international rescue loans for the past two and a half years, after it admitted its budget deficit was more than three times the initial forecast and swiftly lost access global bond markets. In exchange for the funds, the government repeatedly slashed incomes and raised taxes to tame the deficit, creating widespread public resentment that sparked countless strikes and protests — many violent.
On Wednesday, several hundred municipal workers protesting against plans to force redundancy on some civil servants were stopped by police from breaking into the grounds of Parliament in central Athens.
Inside the building, Parliament employees held a three-hour work stoppage to protest a new tax bill due to be presented Friday. Unionists said they were planning further action in coming days, which could disrupt legislative work.
Sarah DiLorenzo in Brussels and Elena Becatoros in Athens contributed.Suggest a correction