Greek Cypriot leader Nicos Anastasiades and his Turkish Cypriot counterpart Dervis Eroglu have agreed to work towards a new system of power-sharing.
The agreement came as talks aimed at ending a bitter conflict resumed after a two-year break.
The meeting took place in the UN-controlled buffer zone at the now defunct Nicosia international airport.
The two groups said they would seek to forge a two-zone federation reuniting the island, which has been split for almost 40 years.
"The leaders expressed their determination to resume structured negotiations in a results-oriented manner," said UN envoy Lisa Buttenheim.
The chief negotiators from both sides will visit Greece and Turkey in the coming days to push the process forward.
The island's untapped gas and oil riches offshore and a huge natural gas find in waters off neighbouring Israel have changed the dynamics in the region.
Hope is high that these factors can transform the current frosty climate into one of reconciliation and trust that would make an elusive peace deal achievable.
Cyprus has been divided since Turkish troops invaded and occupied its northern third in 1974 in response to an Greek-engineered coup.