Left-wing Cypriot leader Demetris Christofias has won the presidential election and promised to work on re-uniting the divided island.
Christofias has already arranged to meet the Turkish-Cypriot president
He defeated rival right-winger Ioannis Kasoulides in a second round of voting.
Cyprus has been divided since 1974 when Turkey sent troops into the north after a coup by Greek Cypriots designed to produce union with Greece.
Turkish-Cypriot leader Mehmet Ali Talat telephoned Mr Christofias to congratulate him on his victory.
The two men agreed to meet "at the earliest possible date" for discussions on the status of Cyprus, a spokesman for Mr Talat said.
For his part, Mr Christofias told a stadium full of exuberant supporters that he "extended a hand of friendship to my compatriots the Turkish Cypriots and their political leadership".
"I call on them to work together for our common cause, a country of peace," said the 61-year-old president-elect.
The defeated Mr Kasoulides congratulated his rival and offered to help find a solution to the division of Cyprus.
The two men had emerged neck-and-neck from the first round of the election, which saw the defeat of President Tassos Papadopoulos.
Official figures showed Mr Christofias, who heads the communist Akel party, won 53.36% of the vote to Mr Kasoulides' 46.64% in Sunday's second round.
Akel supporters celebrated victory outside the party headquarters in Nicosia, chanting slogans and waving flags. Car horns could be heard across the city.
"Tomorrow is a new day and there will be many difficulties before us," Mr Christofias told supporters.
"We need to gather our strength to achieve the re-unification of our homeland."
The Turkish Republic of Northern Cyprus is only recognised by Turkey.
UN forces patrol a buffer zone across the island.
Mr Christofias told supporters he aimed to reunite Cyprus
The island's partition along ethnic lines has long stood as an obstacle to Turkey's bid to join the EU, and remains a source of contention between Nato allies Turkey and Greece.
Mr Christofias is likely to find that any progress on re-unification will be slow and difficult, says the BBC's Tabitha Morgan in Nicosia.
Many sensitive issues remain unresolved, including the return of refugees, security and the constitution.
The president-elect has already made an alliance with the party of the defeated Mr Papadopoulos - the man who firmly rejected the last UN plan to solve the Cyprus problem.