The deal to reunify, which is to happen before its 1 May entry into the EU, caps three decades of failed diplomacy over the Mediterranean island.
The agreement crowned three days of negotiations in New York in which UN Secretary-General Kofi Annan pressed the leaders to demonstrate their will to resolve the impasse on the island, split into ethnic Greek and Turkish enclaves since a 1974 invasion of the north by Turkey.
"Following three days of meetings and consultations, I am pleased to announce that the parties have committed to negotiations in good faith on the basis of my plan," a beaming Annan said at a news conference in the United Nations headquarters in New York.
But all sides warned of the potential pitfalls ahead.
"There is still a lot of work to do. It is not all over yet. We must all be very careful. For a lasting peace, the realities of the island must be taken into account," Turkish Foreign Minister Abd Allah Gul told reporters in Ankara, Turkey's capital.
The stakes could not be higher for both Cyprus and Turkey. Without a settlement, Cyprus would enter the European Union on 1 May as a divided island and be represented only by the internationally recognised Greek Cypriot government.
The talks had deadlocked mainly over the Greek Cypriot side's (led by Tassos Papadopoulos) insistence on bringing European Union experts into the negotiation process, a proposal the Turkish Cypriot side strongly opposed.
"There is still a lot of work to do. It is not all over yet. We must all be very careful"
Abd Allah Gul,
Foreign Minister, Turkey
But an overnight barrage of diplomacy by the United States and Britain, the former colonial power, convinced the Greek side to back down, diplomats close to the talks said. US Secretary of State Colin Powell and British Foreign Secretary Jack Straw personally made calls, they said.
Ankara, whose own efforts to start talks to join the European Union hinge on the Cyprus peace process, had also been pushing Turkish Cypriot leader Rauf Denktash to reach a deal.
In a compromise, the final pact allowed European Union experts to participate in a technical committee on financial and economic matters. Another key sticking point was resolved when both sides agreed to let Annan fill in any gaps in a final agreement on which the two sides deadlocked.
In case of deadlock by a 22 March deadline, Turkey and Greece would be brought in for a week of intensive negotiations, and if that failed, "I have the right to complete the plan," with a goal of a final text by 29 March, Annan said.