Nearly 177,000 voters were eligible to participate in the second round of elections.
The committee said official results will be announced later on Sunday night.
Eroglu congratulated his successor, who will be the fourth president of the country and will serve a five-year term, saying he was ready to exchange views with Akinci over peace talks with Greek Cypriots.
Eroglu also thanked his supporters and said that Sunday`s presidential bid was his last political election. However, he said that he would continue to express his ideas and thoughts over policy.
Negotiations between the TRNC and the Greek Cypriot administration had resumed after a two-year pause in February 2013.
However, the Greek Cypriot administration suspended the talks over the divided island on Oct. 7, 2014 after Turkey sent a ship to monitor an oil-and-gas exploration mission off the coast of Cyprus.
In October 2014, Turkey and the Turkish Cypriot government strongly opposed any "unilateral" move by the Greek Cypriot side to explore for hydrocarbon resources around the island, saying its natural resources should be exploited in an equitable manner under a united Cyprus.
The Turkish Cypriot government has repeatedly said that the resources of the island of Cyprus belong to both communities, and that the Turkish Cypriots would not give up their rights to the resources.
Greek Cypriot leader Nicos Anastasiades and UN special adviser on Cyprus Espen Barth Eide congratulated Akinci over the phone, a statement issued by Akinci`s office said.
Eide is due to visit the island on May 4 for the resumption of negotiations, calling 2015 the year of "opportunity,” the statement added.
The 67-year-old president-elect served as chairman of the Communal Salvation Party (TKP) between 1987 and 2000.
Akinci also served as deputy prime minister and tourism minister between1999-2001. He was a lawmaker in parliament between 1993-2009.
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