The International Court of Justice (ICJ) said it would start the hearings on December 2, as it weighs a so-called advisory opinion on global climate change.
In March 2023, the UN asked the ICJ to clarify "legal consequences" for states that "have caused significant harm to the climate system and other parts of the environment".
It specifically asks the court to weigh obligations to "small island developing States", which are "particularly vulnerable" to climate change, as well as obligations to future generations.
Vanuatu, a small archipelago whose future is threatened by rising sea levels, had been pushing for this resolution for years.
Although ICJ opinions are not binding, they carry significant legal and moral weight, and are often taken into account by national courts.
Vanuatu and its supporters hope the ICJ opinion, which will take months if not years to formulate, will encourage governments to accelerate actions to halt climate change.
China and the United States, the world's two largest emitters, were not co-sponsors of the UN request to the ICJ. US representative Nicholas Hill said at the time he preferred diplomacy to a "judicial procedure".
"We have serious concerns that this process could complicate our collective efforts and will not bring us closer to achieving these shared goals," said Hill.
The ICJ hearing will be another high-profile event in a growing effort to enshrine climate justice in international law.
In what was hailed a "historic" judgement in May, the UN maritime court ruled in favour of nine small island states seeking to increase protection of the world's oceans.
Polluting countries had a "specific obligation to take all measures necessary to ensure that... emissions under their jurisdiction or control do not cause damage by pollution to other states and their environment", that court said.
However, the ICJ ruling is not likely to happen immediately -- the time limit for filing written observations has already been extended several times since April 2023, when the court fixed an initial six-month deadline.
In total, 91 written statements on the subject have been filed with the court, it said.