North Korean leaders, who have been subject to some of the world's toughest ever sanctions, have long wanted to meet with the US president, in part because of the worldwide legitimacy such a summit would provide.
Trump and Kim landed in a city teeming with media and onlookers of all stripes, from foreign policy analysts like Kelly and Enos to former basketball star Dennis Rodman, who claims to be a friend of the two leaders.
The sense of anticipation was palpable as Mr Trump headed to meet Singapore's Prime Minister Lee Hsien Loong on Monday, with people lining the streets waving cell phones.
While en route to Singapore, Trump said he looked forward to meeting Kim on what he anticipated would be an exciting day.
Just meeting with Mr. Trump will also give Kim a recognition North Korea has long sought, setting him up as global player and equal to the USA domestically and, internationally, as the leader of a "normal country" worthy of respect.
Earlier, North Korean media confirmed that Washington and Pyongyang will discuss denuclearisation.
Last year, the North made one of the biggest breakthroughs in its missile and nuclear weapons programs - which it says it needs to defend against the risk of a US invasion - when it announced that it had "completed" its state nuclear program after testing a missile capable of striking most, if not all, of the continental U.S.
Trump initially touted the potential for a grand bargain with North Korea to rid itself of a nuclear missile programme that has advanced rapidly to threaten the United States, insisting he would swiftly achieve what previous US administrations have failed to do.
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The North has presented Kim's sudden diplomatic overtures to the country's neighbours and the USA as a logical next step and completion of his plan to develop a credible nuclear deterrent in response to what Pyongyang says is a policy of "nuclear blackmail" by Washington.
That may be even more important to Trump in the wake of the disastrous G-7 summit.
A smiling Kim Jong Un has been pictured enjoying a late-night stroll in Singapore ahead of his landmark meeting with Donald Trump.
Al Jazeera's Adrian Brown reports from Singapore.
"I think we should take some optimism from that reporting", the official said. "We're not going to go in and sign something on June 12, and we never were".
He told reporters he would "know within a minute" whether Mr Kim was serious about giving up his nuclear weapons.
The president who once described Kim as "Little Rocket Man" and threatened to destroy his country if it did not give up nukes, has not said what might happen if the summit goes the wrong way.
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