Eurozone finance ministers and the IMF have reached a deal on an urgently needed bailout for debt-laden Greece.
They have agreed to cut debts by 40bn euros ($51bn; £32bn) and have paved the way for releasing the next tranche of bailout loans - some 44bn euros.
Greek Prime Minister Antonis Samaras welcomed the deal, saying "a new day begins for all Greeks", but it was condemned by the main opposition party.
European and Asian shares and the euro all climbed on news of the agreement.
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The German Dax and French Cac 40 indexes each rose by 0.8% at the start of trading on Tuesday, while in London the FTSE 100 gained 0.6%, reversing losses from Monday.
In Asia, the MSCI's broadest index of Asia Pacific shares outside Japan gained 0.3% to its highest level in more than two weeks. Australian shares rose 0.7%, while South Korea's benchmark Kospi index was up nearly 0.9%.
The euro reached its highest level against the dollar since 31 October, up about 0.2% to $1.30.
The breakthrough came after more than 10 hours of talks in Brussels. It was the eurozone's third meeting in two weeks on Greece.
The deal opens the way for support for Greece's teetering banks and will allow the government to pay wages and pensions in December.
The leader of the eurozone finance ministers' group, Jean-Claude Juncker, said Greece would get the next instalment of cash on 13 December.
Greece has been waiting since June for the tranche, to help its heavily indebted economy stay afloat.
European Central Bank (ECB) president Mario Draghi said the bailout would "strengthen confidence in Europe and in Greece".
For his part, Mr Juncker said the deal did not just have financial implications.
"This is not just about money. It is the promise of a better future for the Greek people and for the Euro area as a whole."
Greece's international lenders have agreed to take steps to reduce the country's debts, from an estimated 144%, to 124% of its gross domestic product by 2020.
These include cutting the interest rate on loans to Greece, and returning 11bn euros to Athens in profits from ECB purchases of Greek government bonds.
Ministers have also agreed to help Greece buy back its own bonds from private investors.
So far the ECB, IMF and the European Commission have pledged a total of 240bn euros in rescue loans, of which Greece has received around 150bn euros.
In return, Greece has had to impose several rounds of austerity measures and submit its economy to scrutiny.
The European Union's commissioner for economic and monetary affairs, Olli Rehn, said it was crucial that a deal had finally been reached.
"For the eurozone this was a real test of our credibility, of our ability to take decisions on the most challenging of issues.
"And it was a test that we simply could not afford to fail."
However, the Greek radical left opposition party Syriza - who came close to winning elections earlier this year - rejected the deal.
"It's a half-baked compromise, a band-aid on the gaping wound of Greece's debt," said Syriza deputy Dimitris Papadimoulis, who claimed that the German Chancellor Angela Merkel had blocked attempts to cut Greece's debt in half.