UNITED NATIONS — The United Nations secretary general, Ban Ki-moon, is expected to announce on Wednesday that he has secured enough commitments from world leaders to ensure that the 2015 Paris climate accord will enter into legal force this year, binding the next American president, whoever it is.

The milestone is in reach in large part because Mr. Ban, who sees the climate deal as a centerpiece of his legacy, began a sustained push to win the formal approval of 55 countries representing 55 percent of global emissions — the threshold needed to put the accord into force. He pressed the issue personally with dozens of world leaders and with legislative bodies, including those in Russia and his native South Korea.

“We are absolutely certain that we will have the Paris agreement entering into force by the end of 2016,” said David Nabarro, a special adviser to Mr. Ban.

Complex and controversial international accords usually take several years to enter into legal force. But the haste on the Paris accord was driven at least in part by the looming American election. Donald J. Trump, the Republican candidate, has vowed to pull the United States out of the accord if he is elected. If the deal comes into legal force before the presidential inauguration, it will take four years under the accord’s rules for the United States to legally withdraw. That would keep the country bound to the measure through the first term of the next administration.