The statement said a first meeting between the leaders is planned for the beginning of next week.
Cyprus was divided in 1974 when Turkey intervened after a coup by supporters of union with Greece.
The most recent round of talks, which aimed at forging a federation between the Turkish Cypriot north and the internationally recognized Greek Cypriot south, ground to a halt in the middle of 2012.
The two sides have been haggling over the wording of the joint declaration for several months. In a departure from previous failed rounds of negotiations, the island's Greek Cypriot President Nicos Anastasiades insisted that the declaration had to precede any resumption of talks in order to ensure both sides were on the same page.
The main point of contention had been on the sovereignty status of a reunified Cyprus amid concerns among Greek Cypriots that Turkish Cypriot leader DerviÅŸ EroÄŸlu was seeking recognition for his community as a separate state that would act as a buffer against domination by the majority Greek Cypriots. But Greek Cypriots argued that would plant the seeds of permanent partition in case any new arrangement collapsed.
Anastasiades said the draft declaration "safeguards the important principles and basis for a solution."
"The hardest part is yet to follow," Anastasiades said after talks with Greek Prime Minister Antonis Samaras in Athens Friday. "The joint declaration doesn't constitute the solution to the Cyprus problem, but sets the parameters along which the two communities must move."
Debt-laden Greek Cyprus agreed last year to a bailout with its euro partners and the International Monetary Fund. A peace deal could reap a huge financial dividend.
After months of stalemate, things began moving rapidly earlier this week following a visit to Greek Cyprus by US Undersecretary of State Victoria Nuland.
On Friday, Anastasiades spoke to US Vice President Joe Biden who according to Greek Cypriot officials expressed "unwavering US support for a just and lasting settlement." They said Biden was encouraging "creative thinking" to boost the chances of success.