Tatar, 60, clinched his victory on Sunday winning a run-off election against incumbent Mustafa Akinci, with 51.7 percent of the ballots.
In his victory speech, Tatar, who served as the premier of the self-proclaimed Turkish Republic of Northern Cyprus said the people wanted their own independent state.
"The world should now respect the fight of Turkish Cypriots to live independently and honorably under its own roof," he asserted.
Turkey is the only country that recognizes Northern Cyprus.
Tatar called on the world community to recognize the Turkish Republic of Northern Cyprus and respect its people's "fight for freedom."
"We are fighting to exist within the Turkish Republic of Northern Cyprus, therefore our neighbors in the south and the world community should respect our fight for freedom," the right-wing nationalist leader said.
"We deserve our sovereignty -- we are the voice of Turkish Cypriots," he noted.
Tatar thanked Turkey's President Recep Tayyip Erdogan for his support.
"They will never tear the ties between us and Turkey," he said.
Erdogan took to Twitter to relay his congratulations before calling Tatar.
"I congratulate Ersin Tatar who has been elected president... Turkey will continue to provide all types of efforts to protect the rights of the Turkish Cypriot people," he wrote on Twitter.
According to Erdogan's office, the two leaders discussed on the phone the broadening of ties between Ankara and Nicosia in all social, economic and military areas, "starting with the hydrocarbon linked activities in the Eastern Mediterranean."