"This is a historic day for conservation and a sign that in a divided world, protecting nature and people can triumph over geopolitics," said Greenpeace's Laura Meller.
EU environment commissioner Virginijus Sinkevicius on Sunday called the treaty "a crucial step forward to preserve the marine life and biodiversity that are essential for us and the generations to come."
Following two weeks of intense talks, including a marathon overnight session Friday into Saturday, delegates finalized a text that now cannot be significantly altered.
"There will be no reopening or discussions of substance," Lee told negotiators.
The agreement will be formally adopted at a later date once it has been vetted by lawyers and translated into the United Nations' six official languages, she announced.
UN Secretary-General Antonio Guterres commended the delegates, according to a spokesperson who said the agreement was a "victory for multilateralism and for global efforts to counter the destructive trends facing ocean health, now and for generations to come."
The high seas begin at the border of countries' exclusive economic zones, which extend up to 200 nautical miles (370 kilometers) from coastlines. They thus fall under the jurisdiction of no country.
Even though the high seas comprise more than 60 percent of the world's oceans and nearly half the planet's surface, they have long drawn far less attention than coastal waters and a few iconic species.
Ocean ecosystems create half the oxygen humans breathe and limit global warming by absorbing much of the carbon dioxide emitted by human activities.
But they are threatened by climate change, pollution and overfishing.
Only about one percent of the high seas are currently protected.
When the new treaty comes into force it will allow the creation of marine protected areas in these international waters.
"High seas marine protected areas can play a critical role in building resilience to the impact of climate change," said Liz Karan of The Pew Charitable Trusts, which called the agreement a "momentous achievement."
The treaty will also oblige countries to conduct environmental impact assessments of proposed activities on the high seas.
A highly sensitive chapter on the sharing of potential benefits of newly discovered marine resources was one of the focal points of tensions before it was finally overcome as the scheduled talks, due to end Friday, overran by a day.
Developing countries, without the means to afford costly research, had fought not to be excluded from the expected windfall from the commercialisation of potential substances discovered in the international waters.
Eventual profits are likely from the pharmaceutical, chemical or cosmetic use of newly discovered marine substances that belong to no one.
As in other international forums, notably climate negotiations, the debate ended up being a question of ensuring equity between the poorer global South and richer North, observers noted.
In a move seen as an attempt to build trust between rich and poor countries, the European Union pledged 40 million euros ($42 million) in New York to facilitate the ratification of the treaty and its early implementation.
The EU also announced $860 million for research, monitoring and conservation of oceans in 2023 at the Our Ocean conference in Panama that ended Friday. Panama said a total of $19 billion was pledged by countries.
In 2017, the UN General Assembly adopted a resolution calling on nations to establish a high seas treaty.
It originally planned four negotiating sessions but had to pass two resolutions to ensure two additional sessions.
"We can now finally move from talk to real change at sea," said Greenpeace's Meller.