New Democracy, which came top, has backed the two bailouts of Greece by the European Union (EU) and International Monetary Fund (IMF).
There had been fears that if anti-bailout party Syriza had won, Greece could have been forced out of the euro.
France's main Cac index was up 1.8%, while Germany's Dax added 1.5%. Asian shares had earlier also advanced.
Japan's Nikkei 225 index and South Korea's Kospi both closed up 1.8%, while Australia's ASX 200 added 1.9%.
The UK's FTSE 100 was up 1.3%.
Antonis Samaras, the leader of the New Democracy party, 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."
'Sense of relief'
The elections in Greece were being watched closely not just by eurozone leaders but also investors all across the globe.
Greece, which is suffering from a sovereign debt crisis, has received two bailouts in the past two years.
It was given an initial package worth 110bn euros (£89bn; $138bn) in 2010, followed by another one last year worth 130bn euros.
However, the EU and IMF have attached tough austerity measures, including state spending cuts, as pre-conditions to those packages.
There have been various demonstrations against those cuts in Greece and the Syriza party had said that it would renegotiate the conditions if it came to power.
It had led to fears that if eurozone leaders and Athens did not agree on the existing terms, Greece may be forced to leave the eurozone.
There were concerns that such a move may spread contagion to other eurozone countries and result in turmoil in the global economy.
Analysts said that because the highest number of voters had backed the pro-bailout New Democracy party, those fears had been allayed for now.
"There'll be a definite sense of relief spreading around today," said Masayuki Doshida a senior market analyst at Rakuten Securities.
The gains were not limited to stockmarkets.
The euro rose almost 1% against the US dollar, hitting a one-month-high of $1.2748 in early Asian trade.
Analysts said that even though the crisis in Greece has not been solved, the result of the elections had made some investors optimistic that it may have bottomed out.
"At some point in time, when the crisis does end, there will be a significant move of capital from across the world back into the EU," David Lennox of Fat Prophets told the BBC.
"We think that early punters are already taking the view that a floor has been put under the crisis for now."
The price of oil also jumped, boosted by a weakening dollar and on hopes that consumer demand may pick up should stability return to the eurozone.
Brent crude rose 1.5% to $99.11 per barrel, while US light crude rose more than 1% to $84.97 per barrel.
Some analysts said that investors should treat the gains in the markets with caution.
"The markets have become extremely reactive," Mark Matthews, head of Asia research at Julius Baer, told the BBC.
He said while the Greek elections had allayed fears about the country leaving the eurozone, the debt crisis still needed to be resolved.
There have been differences among leaders and policymakers about what is the best way to solve the crisis and spur growth in the region.
Mr Matthews said that until a sustainable solution can be found, markets were likely to remain volatile.
At the same time, some analysts were of the view that concerns about debt problems in larger economies such as Spain may resurface and hurt market sentiment.
Spain's borrowing costs rose to another euro-era record last week, indicating that lenders were concerned about Madrid's ability to repay its debt.
The yield on benchmark 10-year bonds rose as high as 7% in early trade on 14 June, a level which many analysts believe is unsustainable in the long term.
Even though the yield fell back slightly later in the day, analysts fear that the country may have to pay even higher interest rates while raising money in the near future.
The ratings agency Moody's cut Spain's credit rating to one notch above "junk" last Wednesday.
"How long is it going to take for people to worry about Spain again?" said Peter Schiff of the brokerage Euro Pacific Capital.
Last edited by Rizmi on Mon Jun 18, 2012 2:02 pm; edited 1 time in total