Royal said the strength of support meant the climate deal clinched in Paris last year would likely be ratified in New York on April 22.
Almost 200 governments reached an agreement in December which set a target of limiting global warming to "well below" 2.0 degrees Celsius (3.6 Fahrenheit) compared to pre-industrial levels.
"I fixed an objective... of a hundred signatures and we are now at over 120 signatures," Royal, who took over as head of the COP21 this year, told a press conference in Paris.
Garnering a "record number of signatures with such a brief delay... will allow us to begin the ratifications".
COP21 is the acronym for the 21st conference of parties to the UN climate arena.
The 32-page deal also calls on rich nations to muster at least 100 billion dollars (90 billion euros) a year in climate aid from 2020. Just how that will happen has yet to be worked out.
The deal only comes into force, however, if at least 55 countries responsible for at least 55 percent of global greenhouse gas emissions ratify the accord.
Top emitters the United States and China will be among the nations signing the Paris climate agreement in New York, the White House announced last week.
The European Union also agreed to sign last month, and Royal said another key developing country, India, had also agreed.
"We have also received commitments from practically all the African countries," she added.
Royal, heads the UN's COP21 climate forum and thus plays a key role in brokering agreements, said that 60 countries would send their head of state to the signing ceremony in New York.
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