Centre-right leader Nicos Anastasiades has won the Cypriot presidential election with 57.5% of the vote.
It was a comfortable victory over Communist-backed Stavros Malas on 42.5%. Mr Malas has conceded victory.
Mr Anastasiades takes power as Cyprus stands on the brink of bankruptcy, hit by the knock-on effect of Greece’s economic woes.
He favours a quick deal with foreign lenders to finalise a bailout of the Cypriot economy.
“It is a clear and strong mandate for change, for reform, for our country to exit this vicious circle of crisis,” Tasos Mitsopoulos, Mr Anastasiades’s spokesman, told reporters according to Reuters news agency.
Jubilant supporters of Mr Anastasiades’s Democratic Rally party waved Greek and Cypriot flags, honked car horns and set off firecrackers in the capital Nicosia as the results came in, said reports.
But Mr Malas warned his party would be “severe critics of anything that diverts from the interest of the people or the country”, said AFP news agency.
The Cypriot economy is in recession and the state has little money in its accounts.
Cyprus first asked the EU for a bailout last July to shore up its banks.
Because of the bailout deal for Greece, and the restructuring of its debts, which saw private bondholders suffer big losses, Cypriot banks lost about 75% of their investments.
However, the Cypriot bailout deal has foundered in protracted negotiations.
The new president will have to finalise a deal with the other 16 countries that use the euro and with the International Monetary Fund (IMF).
Mr Malas supported a bailout but opposed austerity. Last week’s first round in the presidential election failed to produce a decisive result.
Mr Anastasiades will aim to exploit massive natural gas finds off Cyprus’s coast, bringing in badly needed income and energy, but risking escalating tensions with Turkey, says the BBC‘s Mark Lowen in neighbouring Greece.
He will also be under pressure to reach out to Turkish Cypriots in the north of the island, cut off since Cyprus was formally divided along ethnic lines almost four decades ago, our correspondent says.