At stake are oil and gas fields estimated to be worth tens of billions of dollars.
Australia's refusal to negotiate a permanent maritime border with Timor-Leste has strained relations.
The fledgling country's request for compulsory negotiations with its neighbour to decide the boundaries of large oil and gas fields was opposed by the Australian government last month.
But the United Nation's Conciliation Commission in The Hague overruled Australia's protest last night, ordering it to take part.
The decision has been welcomed by Timor-Leste's Minister of State, Agio Pereira, in an interview with the ABC.
"It's good for both Australia and Timor Leste, that's very good. Because you have to resolve these issues. You cannot go on forever arguing with each other in a polarised way."
Foreign Minister Julie Bishop and Attorney-General George Brandis have issued a statement saying Australia accepts the Commission's decision and will continue to engage in good faith in the conciliation process.
The Opposition wants a quick resolution.
Labor's foreign affairs spokeswoman, Penny Wong, says a permanent agreement is long overdue.
"This is an opportunity for us to resolve it. To settle these maritime boundaries in fair and permanent terms. And we would urge the government to take this opportunity with both hands."
Under current treaty arrangements, revenue from the Joint Petroleum Development Area in the Timor Sea is split.
90 per cent goes to Timor-Leste and 10 per cent to Australia.
If the maritime boundary were to be drawn half-way between the two countries, the rich oil and gas fields would fall entirely in East Timorese waters.
An expert on Timor-Leste at Deakin University, Professor Damien Kingsbury, says the federal government may fear being asked to pay back royalties.
"There is also concern that it could open up the possibility of Indonesia also asking for its boundaries to be redrawn in line with the international law of the sea."
The Commission's report will not be legally binding.
A Timor Leste specialist at Melbourne's Swinburne University of Technology, Professor Michael Leach, says Australia's response will be watched internationally.
"Australia has taken quite a strong position on China in the South China Sea, urging them to respect international law, which obviously raises the issue of consistency in relation to this dispute."
The conciliation process will take place behind closed doors over the next year.
