Anti-austerity Syriza party has won Greece's general election, putting the country on a possible collision course with the EU over its massive bailout.
With nearly 75% of the votes counted, Syriza is projected to win 149 seats, just two short of an absolute majority, though that number could change.
Left-wing party leader Alexis Tsipras, who wants to renegotiate Greece's debt, said "the Greeks wrote history".
The governing centre-right New Democracy has come a distant second.
Outgoing Prime Minister Antonis Samaras has admitted defeat and phoned Mr Tsipras to congratulate him.
Syriza's result will send shockwaves through Europe, the BBC's Gavin Hewitt in Athens reports.
A majority of voters in Greece have essentially rejected a core policy for dealing with the eurozone crisis as devised by Brussels and Berlin, our correspondent adds.
In Germany, Bundesbank President Jens Weidmann said he hoped "the new Greek government will not make promises it cannot keep and the country cannot afford".
The election result is expected to be one of the main issues during Monday's meeting of 19 eurozone finance ministers.
Belgium's representative Johan Van Overtveld was quoted by VRT network as saying that Greece "must respect the rules of monetary union", although he added that there was room for some - but not much - flexibility.
British Prime Minister David Cameron - whose country is not a member of the eurozone - said the result of the Greek election would "increase economic uncertainty across Europe".
Meanwhile, the euro fell to $1.1098 against the dollar - the lowest level in more than 11 years.
'Thing of the past'
Addressing his jubilant supporters in front of Athens' university, Mr Tsipras said Greek voters gave Syriza "a clear, powerful mandate".
"You are an example of history which is changing... Your mandate is undoubtedly cancelling the bailouts of austerity and destruction.
"The troika for Greece is the thing of the past," he added, referring to the country's biggest international lenders - the European Union, International Monetary Fund (IMF) and European Central Bank (ECB).
He also promised to negotiate a fair and mutually beneficial financial solution.
Mr Tsipras earlier vowed to reverse many of the austerity measures adopted by Greece since a series of bailouts began in 2010.
At the scene: BBC's Chris Morris in Athens
On Klathmonos Square, the flags were flying high, supporters of Syriza were singing and dancing, there were hugs and tears and broad beaming smiles.
This was an extraordinary victory for the radical left in Greece - probably beyond its own expectations.
Alexis Tsipras will now try to lead an anti-austerity revolution, backed by a strong democratic mandate.
He said in his victory speech that he is willing to negotiate with Greece's European partners. The question is: how much are they prepared to compromise with him?
For his part, Mr Samaras said earlier: "The Greek people have spoken and I respect their decision," pointing out that he had inherited a "hot potato" on coming into office and that he and his party had done much to restore his country's finances.
The result is being closely watched outside Greece, where it is believed a Syriza victory could encourage radical leftist parties across Europe.
"There is an ongoing thriller surrounding the absolute majority," said Michalis Karyotoglou, head of Singular Logic, the software group monitoring the voting process for the interior ministry.
Either way however, partial results from Greece's election commission showed a clear Syriza lead.
With most votes counted, Syriza is polling 36%, while New Democracy is on 28%.
Another five parties - including the far-right Golden Dawn and centrist The River - are expected to be represented in the 300-member parliament.
The proportion of votes won by smaller parties will have a large impact on whether Syriza can gain the required 151 parliamentary seats to govern with an absolute majority.
Who are Syriza and what do they stand for?
- An acronym meaning the "Radical Coalition of the Left", Syriza was formed in 2004 as an umbrella group
- Led by 40-year-old Alexis Tsipras
- The party first came to prominence following the 2008 Greek riots
- It promises an end to Greece's painful austerity measures and wants to renegotiate its debt
- Markets worry about a Greek debt default and a possible exit from the eurozone, though Syriza says it wants to keep the euro