The global climate change conference in Paris has adopted an international accord aimed at transforming the world's fossil fuel-driven economy within decades and slowing the pace of global warming to well below 2 degrees Celsius.
"I see the room, I see the reaction is positive, I hear no objection. The Paris climate accord is adopted," Mr Fabius declared, adding: "It may be a small gavel but it can do big things."
The new treaty will commence in 2020.
Mr Fabius said the deal would limit global warming - which threatens humanity with rising seas and worsening droughts, floods and storms - to "well below 2 degrees Celsius, perhaps 1.5".
US president Barack Obama was among the world leaders who hailed the deal, which he said marked a "turning point for the world" on climate change."This agreement represents the best chance we have to save the one planet that we've got," he said.
"We came together around the strong agreement the world needed. We met the moment."
Foreign minister Julie Bishop spoke on behalf of the Umbrella Group of Countries, a loose coalition of developed countries not in Europe.
"Our work here is done and now we can return home to implement this historic agreement. This is a pivotal moment," she said.
"No country would see this as the perfect outcome. Certainly it does not include everything that we envisaged. However, this agreement does give us a strategy to work over coming years and decade to build the strong and effective action the world needs."
As he released the final wording, Mr Fabius urged nations to sign up to the treaty saying: "If today we were to fail, how could we rebuild this hope? Trust would be irrevocably lost and beyond that the very credibility of multilateralism and the international community as an entity able to respond to challenges. This is what is at stake."
Setting a broad goal of eliminating the net increase in man-made greenhouse gas emission this century, the agreement does not mandate specific measures or targets.
Instead, it creates a system for ensuring countries make good on voluntary domestic efforts to curb emissions, and provides billions more dollars to help poor nations cope with the transition to a greener economy.
"This text contains the principal elements that we did feel before would be impossible to achieve. It is differentiated, fair, durable, dynamic, balanced and legally binding," Mr Fabius said.
For the first time, a limit of 1.5C has been locked into the treaty after a concerted push by small island nations who said their very existence was threatened if the world limited global warming to 2C.
The treaty said the world will be "holding the increase in the global average temperature to well below 2C above pre-industrial levels and to pursue efforts to limit the temperature increase to 1.5 C above pre-industrial levels, recognising that this would significantly reduce the risks and impacts of climate change".
Kellie Caught from WWF Australia was among the many environment groups that hailed the move.
"By including a long-term temperature goal of well below 2C of warming with a reference to a 1.5C goal, the latest draft text sends a strong signal that governments are committed to being in line with science," she said.
"What we need now is for their actions, including emission reductions and finance, to add up to delivering on that goal."
The United Nations negotiations on climate change have been moving incrementally since 1992.
In 1997 the the world's biggest emitters of climate changing greenhouse gases signed up to the Kyoto Protocol, but it was an agreement always fraught with disagreement.
With its scheduled conclusion in 2012, the world scrambled to find a replacement. The negotiations in 2009, held that year in Copenhagen, were highly anticipated, but ended in chaos and disappointment. In the lead-up to this year's meeting, the French hosts worked hard to avoid the same conclusion.
The standing ovation given to Mr Fabius, the head of the meeting, was testament to the effective progress of the meeting.
Scientists have warned for decades that the increase in carbon dioxide in the atmosphere - largely from burning coal oil and gas - would lead to more of the Sun's heat being trapped on Earth. This year is shaping up to be the hottest year on record, with 2014 the previous record holder.
Outside the plenary on the streets of Paris, thousands of demonstrators wore red to signify the red line they did not want the world to cross.