Asian markets jumped overnight and European exchanges are expected to open strongly after pro-bailout party New Democracy scraped a narrow win at the Greek election.
The election, seen by many as a vote on the euro, was narrowly won by New Democracy, led by Antonis Samaras. He will now be given the opportunity to try to form a coalition government.
Samaras said "the Greek people voted today to stay on the European course and remain in the eurozone".
"There will be no more adventures. Greece's place in Europe will not be put in doubt," he added, promising Athens would "honour its obligations".
The anti-bailout Syriza party, which came a close second, said it would lead the opposition.
With more than 99% of votes counted, interior ministry results put New Democracy on 29.7% of the vote (129 seats), Syriza on 26.9% (71) and the socialist Pasok on 12.3% (33).
New Democracy will try to build a majority coalition with the socialist Pasok, and will benefit from a rule which gives the leading party 50 extra seats in the 300-seat chamber. However, after an inconclusive election six weeks ago, the main parties failed to form a coalition government.
The eurozone crisis will also dominate the G20 Summit of world leaders which starts today in Mexico. They are set to boost the $430bn (£273.6bn) fund being used as a firewall to support struggling eurozone economies.
World markets staged a relief rally on news of the Greek election result. Japan's Nikkei 225 gained 1.7% while South Korea's Kospi Index rose 1.6% and the Hang Seng was up 1%.
However, the Sensex dropped 0.7% after India unexpectedly left interest rates unchanged at 8%, despite inflation concerns.
The euro also rose to its strongest in almost a month to reach $1.2748 before trading at $1.2710 as of 6:44am in London. It sank to $1.2288 on 1 June, the weakest level since July 2010.
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