Shares, the euro and oil all rose sharply on the world's financial markets on Thursday amid signs that Greece had won sufficient support from its private-sector creditors to clinch a new bailout package.

Greek officials reported high levels of take-up by private creditors for the deal. After markets had closed last night one senior government official told Reuters the take-up had been close to 95% an hour before the deadline, more than enough to banish fears that renewed crisis in Greece would hit economic growth and financial markets around the world.

Global stocks enjoyed their best day in more than two months and the euro rose 1.5 cents against the dollar on hopes recession in the eurozone would be short-lived. The cost of crude was up nearly two cents a barrel in London to just over $126.

Traders said there was relief that Greece had won enough support from its private sector creditors to trigger a second bailout – worth €130bn (£109bn) – from the International Monetary Fund, European Union and European Central Bank.

Lorne Baring, managing director of Swiss-based B Capital Wealth Management, said: "The Greek debt restructuring looks set to be passed and sets the scene for an orderly default whereby debts owed by Athens will fall by 2020 to an estimated 120% of GDP. That's another short-term worry out of the way, despite the overlooked fact that this is the biggest sovereign default in history.

"A managed bust is better than a chaotic one and finally reality over Greece's insolvency dawns on the investors who still own its bonds."

The Greek government had been hoping the holders of at least 95% of the country's bonds in private hands would have agreed to the debt swap, which would see them lose more than half their investment, by Thursday night's deadline . But while it appeared that some hedge funds were holding out for better terms, Athens needed only a two-thirds acceptance rate to activate collective action clauses that would force the deal on the vast majority of private investors. Greece's finance minister, Evangelos Venizelos, told the cabinet that the debt swap was "going well".

Dario Perkins, an analyst at Lombard Street Research, said the expected agreement would buy Greece "some additional time, maybe a few months, but it is unlikely to change the end result. Ultimately – as we may have mentioned once or twice before – we expect Greece to default 'properly' and leave the euro area."

The ECB left interest rates unchanged at 1% as it published new forecasts underlining the impact of the sovereign debt crisis on activity in the 17 countries that use the single currency. While the bank's president, Mario Draghi, said a deal was "very close", his economic staff said they now expected eurozone growth this year of between -0.5% and 0.3% (down from a previous forecast of between -0.4% and 1%). In 2013, they forecast growth of between 0% and 2.2% (down from between 0.3% and 2.3%)

On inflation, the ECB expects the consumer price index to be between 2.1% and 2.7% (from 1.5% to 2.5%). Analysts said the pick-up in inflation ruled out further cuts in the cost of borrowing.

Economic data for Greece itself showed that more than half of those (51.1%) aged between 15 and 24 were unemployed – a doubling in the past three years. The overall jobless rate hit 21% in December 2011.

Although many economists fear that the crisis in the eurozone is far from over, the mood in the financial markets was upbeat. The FTSE 100 finished 68 points higher at 5859, up almost 1.2%. The French CAC and the German DAX enjoyed stronger rallies, both finishing 2.5% higher. Shares on Wall Street rose in morning trading, with sentiment boosted both by developments in Greece and by hopes that today's US unemployment report will show the world's biggest economy finally emerging from the financial crisis and economic slowdown of the past five years.

Dan Dorrow, director of research at Faros Trading in Stamford Connecticut, said: "By Greece avoiding a disorderly default it will remove a key risk hanging over the markets over the next few weeks."