The meeting, long sought by Pyongyang, will be the first ever between a serving US President and a North Korean leader, and will focus on the nuclear bombs and ballistic missiles the North has spent decades developing.
Heavy security and armed police are standing guard at summit-related venues across the city state.
Kim Jong Un (centre) arrives at Marina Bay Sands on the eve of the historic USA and North Korea summit.
The opening bid from the United States is the full and comprehensive dismantlement of North Korea's nuclear weapons infrastructure, from the warheads stored in the underground depots to the facilities that churn out the enriched uranium and the reprocessed plutonium. At the same time, he'd admitted he didn't believe he required extensive preparation to take stock of Kim.
Trump said Tuesday after meeting Kim that he's feeling "really great". The North Korean approach, he added was: "Let's be friends (ie, change the relationship), and then we will change our behaviour".
The team of White House aides and Trump administration officials had not mentioned whether the issue of North Korean human rights will be addressed during the summit between the two leaders, a sign the United States' priorities lie in mitigating weapons threats.
Washington is demanding the complete, verifiable and irreversible denuclearisation (CVID) of North Korea.
But some question why Kim should trust any guarantees given Trump's history of pulling out of accords - most recently the painstakingly negotiated Iran nuclear deal.
He smiled at citizens who cheered for him.
The front page of the June 12 Rodong Sinmun contains a short story and over a dozen photos detailing Kim's night stroll through downtown Singapore late Monday night, which took place less than twelve hours before the article appeared on the newspaper's website. "If they don't denuclearise, that will not be acceptable", Mr Trump said ahead of the meeting.
"China might have wanted to prevent Chinese smugglers from entering North Korea so they cracked down on smuggling organizations in the border area few days ago and arrested number of smugglers", he said.
While advisers say Trump has been reviewing briefing materials, the president insists his gut instincts will matter most when he gets in the room with Kim. But Trump's off-the-cuff negotiating style - and his growing disregard for many of Washington's closest allies - makes it hard to predict what any such a deal might include. It's aimed at settling a standoff over Pyongyang's nuclear arsenal.
Talks proceeded at multiple levels, including logistical discussions to allay Kim's fears of being deposed while traveling further afield than he ever has before as the country's leader. It was a striking about-face from less than a year ago, when Trump was threatening "fire and fury" against Kim, who in turn scorned the American president as a "mentally deranged US dotard". "If Trump gets something about this, it will boost his agenda".
Amateur body language analysts noted that Trump is being more physical than Kim. Some have criticized Trump for holding the meeting, claiming that he is giving legitimacy to a murderous dictator and that he agreed to a meeting before North Korea gave any real concessions.
The lead-up to the summit has been marked by uncertainty and waves of frenetic diplomacy - at one point, Mr Trump even briefly called off the summit, after a senior North Korean official described remarks by US Vice-President Mike Pence as "stupid".