Trump accepted an invitation late Thursday to meet with Kim for nuclear talks by May.
In a "Squawk Box" interview, Burns credited Trump's veiled military threats in response to Kim's aggression and diplomatic progress with North Korean ally China for seeding an environment to make a meeting possible.
"President Trump has had some impact on China. The Chinese have done more on the last year than they had done previously," Burns said. He also said the Trump administration has also been able to get "bigger sanctions, stronger sanctions and resolutions out of the U.N."
"President Trump has kept Kim Jong Un off balance," said Burns, whose 27-year career in foreign service spanned both Republican and Democratic administrations. "I think this is positive that the president and Kim Jong Un are going to turn towards diplomacy because we were headed for a collision with North Korea."
Burns, who served as U.S. ambassador to NATO and the State Department's third-ranking diplomat during George W. Bush's presidency, said he never thought a meeting between the two nations would ever take place. "This is going to be biggest moment of the Trump presidency."
"This is a real shocker. This is a real surprise," added Burns, who also advised the administrations of George H.W. Bush and Bill Clinton. "There's never been a meeting between a North Korean leader and an American leader going all the way back to the late 1940s when North Korea was formed."
Despite the optimism, Burns said the U.S. needs to go into this meeting with a skeptical bearing and clear goals for what's possible to defuse North Korea's nuclear ambitions.
"[Kim], his father, and grandfather have played the United States and South Korea before," Burns said. "[Kim] is in a very strong position. He has nuclear weapons. He's made progress on his nuclear and missile tests."
Burns pointed out that the U.S. had agreements with North Korea in the Clinton and George W. Bush administrations.
"They burned us," said Burns, currently a professor at the Harvard Kennedy School of Government. He urged Trump and Secretary of State Rex Tillerson to make sure to get "verification at every step" and to get South Korea, Japan, and China in "completely united in lock step."
However, Burns warned that Kim may not be looking to make subsitive concessions. "They want legitimacy. They want acceptance. I think they want to keep the nuclear weapons."