There is however no detail on how some of the contentious issues, such as shifting the seabed boundary, will be resolved.
"There are many details still to be worked through by the two sides. Another meeting will be held in the very near future, but I am confident that we are on the brink of securing an agreement to handle for a long period our competing claims in the Timor Sea, and in turn unlock the enormous hydrocarbon potential of this region," said Ramos-Horta.
"The constructive approach adopted at this week's talks has led to very positive progress in resolving the Timor Sea dispute. This puts our two nations on the threshold of a new era in bilateral relations and economic cooperation.
"Finding ways to allow the development of petroleum resources will bring significant economic benefit to both nations. Timor-Leste, which is one of the poorest nations in the world, stands to benefit enormously from a final resolution," Dr Ramos-Horta said.
Ramos-Horta was speaking after the conclusion of three days of talks in Dili between delegations from both countries - the fifth in an intensive series of meetings that have been ongoing since September last year.
The next round of talks are scheduled for May 11 in Brisbane.