Finance Minister Evangelos Venizelos hailed the deal, which the nation's international lenders had demanded in return for the 130 billion euro ($172 billion) bailout, as marking a long-awaited success for all Greeks enduring a long recession.
The European Union said the swap, under which private creditors have accepted heavy losses on their Greek bond holdings, would make a "decisive contribution to financial stability in the euro area as a whole".
But markets sharply marked down the value of new Greek bonds to be issued to the creditors, reflecting the risk of paralysis after elections expected this spring and doubts about whether Athens can bring its debt to a more manageable level by 2020.
"Today, after a very long time, is a very good day (for the country) as well as for me personally," Venizelos told lawmakers, saying the deal had cut Greece's debt burden by 105 billion euros.
"I hope everyone will realize, sooner or later, that this is the only way to keep the country on its feet and give it the second historic chance that it needs," said Venizelos, who negotiated Greece's second bailout since 2010 with the European Union and International Monetary in often ill-tempered talks.
Under the biggest sovereign debt restructuring in history, Greece's private creditors will swap their old bonds for new ones with a much lower face value, lower interest rates and longer maturities. This means they will lose about 74 percent on the value of their investments, slicing more than 100 billion euros off Greece's crippling public debt.
The finance ministry said creditors had tendered 85.8 percent of the 177 billion euros in bonds regulated by Greek law. This would reach 95.7 percent of all privately-held Greek debt with the use of "collective action clauses" to enforce the deal on creditors who refused to take part voluntarily.
European Economic and Monetary Affairs Commissioner Olli Rehn, a leading figure in efforts to protect far bigger economies with debt problems such as Italy and Spain, said he was very satisfied with the private creditors' response.
"That contribution by the private sector is an indispensable element to ensure future sustainability of the Greek public debt and, thus, a decisive contribution to financial stability in the euro area as a whole," Rehn said in a statement.
But he told Athens, which has a record of failing to meet its austerity promises, to stick to the bailout's terms.
"I now expect the Greek authorities to maintain their strong commitment to the economic adjustment program and to rigorously and timely implement the policy package," he said. "The success of this program is a cornerstone of our comprehensive response to the current crisis."
Euro zone finance ministers are expected to release the bailout funds next week. Athens must have the money in place by March 20 when some 14.5 billion euros of bond repayments are due, which it cannot hope to repay alone.
Greece remains a long way from solving its daunting economic, political and social problems. Reforms demanded by the EU and IMF along with deep budget cuts have provoked serious violence in Athens and helped propel unemployment well over 20 percent as the nation suffers its fifth year of recession.
The country also faces elections in April or May when the pro-bailout conservatives and socialists face an array of smaller parties to the left and right that reject the rescue, and may struggle to form an effective government.
Traders priced in the profound doubts surrounding an overall program which aims to cut Greece's debt from a towering 160 percent of its annual economic output now to a slightly more manageable 120 percent by 2020.
On the grey market, they indicated prices far below the face value of new bonds which will be issued to creditors on Monday.
Spanish and Italian bond yields fell following the Greek announcement. However, those on debt issued by Portugal, which has also been bailed out by the EU and IMF, rose as investors looked for the euro zone's next weakest link.
The deadline for acceptance of the offer for bonds governed by international law and for state-guaranteed bonds issued by public companies has been extended to March 23.
Athens confirmed it would enforce the deal, activating collective action clauses (CACs) on the bonds regulated under Greek law. It will not be so easy to force holders of bonds governed by foreign laws to come to the table.
Using the CACs is likely to trigger payouts on the credit default swap (CDS) insurance that some investors hold on the bonds. The International Swaps and Derivatives Association said it will meet on Friday at 1300 GMT to decide whether Greek credit default swaps will pay out.
"It almost now certainly going to trigger CDS. If this doesn't trigger it, nothing will," said Nick Stamenkovic, a bond strategist at RIA Capital markets in Edinburgh.
Venizelos played down the consequences. "This is not a concern for us because the net amount at stake globally if CDS are triggered is less than 5 billion (euros)," he told parliament. "This is a totally negligible sum for the Greek and the European economy."