The United Nations said the goal of the negotiations is a bi-national federation "with a single international personality." A Greek "constituent state" and its Turkish counterpart would have equal standing in the federation.
Nicos Anastasiades, president of Cyprus, and Dervis Eroglu, president of the Turkish Republic of Northern Cyprus, met in a U.N. protected area in Nicosia, the capital.
U.N. Secretary General Ban Ki-moon welcomed the talks.
"I commend the leaders for their commitment to resuming negotiations and for their hard work in the past months to reach what is an important statement of shared principles and invaluable basis for renewed talks," Ban said.
Cyprus became independent in 1960 after centuries of control by the Ottoman and British empires. Turkey invaded Cyprus in 1974, seized control of the northern third of the country, and set up a republic that has not been recognized by any other country.
The United States helped kickstart the talks, the Cyprus Mail reported. The two leaders released a joint statement last week, a day after Victoria Nuland, the U.S. assistant secretary of state for European and Eurasian affairs, arrived.
The U.S. State Department hailed the start of the talks in a statement and praised the Greek and Turkish prime ministers, Antonis Samaras and Recep Tayyip Erdogan, for their role in the negotiations.