Mr. Eroglu, the prime minister, won just over 50%, enabling him to avoid a run-off with incumbent, Mehmet Ali Talat, unofficial final results show.
The election may have a major impact on the chances of reuniting the divided Mediterranean island.
Mr. Talat had supported reunification and close ties with the EU.
Results on the Turkish Cypriot High Electoral Board’s website gave Mr. Eroglu 50.38% of the vote to Mr. Talat’s 42.85%. The results still need to be confirmed by the electoral commission.
Mr. Eroglu claimed victory, saying: “We will always work in co-operation with our motherland Turkey.”
However, he told Turkey’s NTV television that “no-one must think that I will walk away from the negotiating table. The talk process will continue”.
“I will work with goodwill for a solution that takes my community’s rights into account,” he added.
Mr. Talat told reporters: “My dream to reach a solution is still there, but of course this is the beginning of a new era.”
Cyprus has been divided since 1974, when Turkish troops invaded in response to a military coup backed by the junta ruling Greece at the time. The breakaway north is not recognized internationally.
Analysts say the result could stall peace talks with the Greek Cypriots and have implications for Turkey’s hopes of fasten together with the EU.
Greek Cypriots, who are already members, could block Turkey’s membership bid.
When Turkish Cypriots voted Mr. Talat into office they had hoped he would unite Cyprus and thus bring to an end decades of international isolation imposed on the unrecognized Turkish Republic in the north of the island, the BBC’s Tabitha Morgan reports from Nicosia.
But despite years of negotiations with the Greek Cypriot leadership, he has not been able to deliver on his promises, she says.
Turkish Cypriots are disappointed and, according to one analyst, wanted “to punish Mr. Talat” for his failure to reunite Cyprus.
Analyze of Tabitha Morgan, BBC News, Nicosia
Mr. Eroglu is strongly opposed to the diplomatic process in which Mr. Talat was engaged seeking to reunify the island.
The Eroglu solution to the long-standing Cyprus problem would involve separate Greek and Turkish Cypriot states, linked by loose confederal ties.
This is totally unacceptable to the majority of Greek Cypriots. So the prospects for a negotiated deal suddenly look significantly worse.
Indeed, Mr. Eroglu’s victory is symptomatic of a mood of disillusionment among most Turkish Cypriots, over Mr. Talat’s failure to make good his promise to reunite Cyprus and end the north’s political and economic isolation.
If no solution to the problem is forthcoming, Turkey’s path towards EU accession will become even more difficult.
CNNNEWS, 18 April 2010