Nearly as if they had rehearsed this moment, Mr Trump entered from the right and Mr Kim from the left.
Inside, they sat alongside each other against a backdrop of North Korean and USA flags, with Kim beaming broadly as the US president gave him a thumbs up.
"It's interesting because we believe Kim speaks English - he was educated in Switzerland and speaks German, but Trump seems to be the only one talking during their bit of chit chat", Professor Hajek told Yahoo7.
After initial exchanges lasting around 40 minutes, Trump and Kim emerged, walking side-by-side through the colonnaded hotel before entering a meeting room, where they were joined by their most senior officials.
Trump is hoping to make a legacy-defining deal that some say could earn him a Nobel Peace Prize.
"It was not an easy journey", Kim said, speaking through a translator. On a larger level, the astronomical cost of the nuclear weapons program contributes to the massive poverty in North Korea, among the world's poorest countries.
"It's going great", Trump said, with Kim at his side.
With a handshake, the leaders of the USA and North Korea broke through decades of antagonism, signaling a willingness to stake their reputations on forging a new relationship between the two nations.
As Trump and Singapore's Prime Minister Lee Hsien Loong sat down for a working lunch at the Istana house, the president sounded optimistic, telling Lee, "We've got a very interesting meeting in particular tomorrow, and I think things can work out very nicely.
We will be tremendously successful", Trump said before their private session.
North Korea has nominally committed to the "complete denuclearization" of the Korean Peninsula, but it has traditionally used that term to also demand that the US remove its assets, including troops, from the region.
Details were not shared about how the discussions have progressed so far and Trump and Kim have yet to meet face-to-face.
Kim has rejected calls to unilaterally give up his weapons in return for economic aid, and instead has proposed a step-by-step denuclearization process.
Top members of Trump's administration have said that the North Koreans wouldn't receive any benefits before taking steps to denuclearize - wary of falling into the same predicament that doomed previous agreements with the rogue regime.
Setting out the U.S. position before the summit, Pompeo stressed that the Trump administration would only accept complete denuclearisation of the North.
The joint document marked the end of the leaders' highly anticipated summit, which opened with both men shaking hands on a red carpet in front of a wall of American and North Korean flags.
But in return, Washington would offer "different and unique" guarantees "to provide them sufficient certainty that they can be comfortable that denuclearisation is not something that ends badly for them".