On Monday, the euro recovered from 11-year lows and Europe's main share markets also rose - after initial falls - on hopes that a compromise over Greece's bailout terms might be found.
"The new Greek government will be ready to co-operate and negotiate for the first time with our peers a just, mutually beneficial and viable solution," Alexis Tsipras, Syriza's party leader, said.
The country's current bailout programme terminates in February, and economists say a short-term deal will be negotiated, although difficult talks lie ahead. Germany has emphasized that it is not prepared to renegotiate the bailout terms, raising the prospect that Greece could end up leaving the eurozone.
"There is a danger of a prolonged stand-off with the troika as Syriza attempts to negotiate some form of official debt restructuring while not reneging on its promises to voters to cut taxes, raise government spending and increase the minimum wage," said Jonathan Loynes, chief European economist at Capital Economics.
Michael Hewson, chief market analyst at CMC Markets, said: "Tsipras's comments don't appear to leave any room for doubt as he stated that the troika and the bailouts belong to the past."
"You can be almost certain that these negotiations will be watched carefully by the anti-austerity movements in Spain, Portugal, Italy and France to see what measures if any Greece is able to get out of EU politicians to deal with the problem of Greece's debt, and the terms of the bailout programme."
George Osborne, he UK Chancellor, urged all sides to "act responsibly" in any forthcoming negotiations over Greece's bailout terms. In an interview with BBC Radio 4's Today programme he told he understood why, with the Greek economy in trouble, voters were "looking for other answers".
However, he warned that Syriza's election promises to spend more on public services and slow the pace of cuts were unlikely to work. "If you take at face value all the things that the new Greek government has promised, including big increases in public expenditure, I think that will be very difficult to deliver," he said.
