Kim arrived in an Air China 747 that touched down at Changi Airport, Singapore's Straits Times said.
Kim Jong-un with Singapore foreign minister Vivian Balakrishnan.
The fighting ended on July 27 1953, but the war technically continues today because instead of a difficult-to-negotiate peace treaty, military officers for the US-led United Nations, North Korea and China signed an armistice that halted the fighting.
The North, many experts believe, stands on the brink of being able to target the entire USA mainland with its nuclear-armed missiles, and while there's deep scepticism that Mr Kim will quickly give up those hard-won nukes, there is also some hope that diplomacy can replace the animosity between the U.S. and the North.
Kim Jong Un has taken only one known overseas trip by air since becoming leader in 2011.
North Korean leader Kim Jong-un arrives at Changi International Airport, on Sunday.
Kim is due to meet Singapore Prime Minister Lee Hsien Loong later on Sunday, Singapore's ministry of foreign affairs said in a statement.
Kim is set to meet Tuesday with Trump in what's shaping up to be one of the most unusual summits in modern history.
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Authorities have beefed up security around the hotels where Trump and Kim (Saint Regis) will be staying in central Singapore. North Korea spent decades developing nuclear weapons, culminating in the test of a thermonuclear device in 2017.
The two countries were on the brink of war previous year, with their leaders trading insults and threats, until Kim made a dramatic offer in March to meet Trump and discuss nuclear disarmament, which the American president quickly accepted. It also successfully tested missiles that had enough range to reach the US mainland. He went out of his way to be cordial during two summits with South Korean President Moon Jae-in in April and May.
Many remain skeptical Kim will ever completely abandon his nuclear programs.
For Kim, almost 40 years Trump's junior and representing the third generation of North Korea's ruling dynasty, the summit affords both him and his long-isolated country the global legitimacy his father and grandfather could only dream of. They believe his latest engagement is aimed at getting the United States to ease crippling economic sanctions that have squeezed the impoverished country.
He has also raised the possibility of further summits and an agreement ending the Korea War by replacing the armistice signed in 1953 with a peace treaty.
The two countries were on the brink of war a year ago, with their leaders trading insults and threats, until Kim made a dramatic offer in March to meet Trump and discuss nuclear disarmament, which the American president quickly accepted.
The two leaders meet at 9 a.m. (0100 GMT) on Tuesday at the Capella on Sentosa island, a refurbished British Army artillery mess that is now one of Singapore's most expensive luxury hotels.