Earlier on Sunday, Trump's Air Force One landed at Paya Lebar Air Base in the central east of Singapore after undertaking a 17-hour long flight from Quebec Canada where he attended the G7 summit.
But it was only Monday morning in North Korea that the government news agency reported that Kim was in Singapore, had met with the prime minister and would meet Trump on Tuesday.
Trump spoke only briefly in public on Monday, forecasting a "nice" outcome.
USA presidents and vice-presidents generally never fly on the same aircraft to guarantee that one of them survives in the event of a disaster, and the move appeared created to ensure the preservation of the Kim dynasty, which has ruled the North for three generations.
The two leaders discussed bilateral relations as well as the summit and the recent positive developments in the Korean Peninsula.
But analysts warn that it risks being more of a media event than an occasion of substantial progress and delegations from the two sides were negotiating at a neutral hotel in Singapore to try to address their differences. Delegates were outlining specific goals for what the leaders should try to accomplish and multiple scenarios for resolving key issues, a senior U.S official said, adding that the meetings were also an ice breaker of sorts, allowing the teams to get better acquainted after decades of minimal contact between their nations.
His sister and close aide Kim Yo Jong is also in Singapore, and is believed to have travelled separately on the ageing Soviet-made Ilyushin-62 that is Kim's personal aircraft.
He and Trump are set to meet Tuesday morning in the first summit of its kind between a leader of North Korea and a sitting US president.
The summit provides "an unprecedented opportunity to change the trajectory of our relationship and bring peace and prosperity" to North Korea, Pompeo told a news conference on the summit's eve.
The area includes the summit venue, Capella Hotel on Sentosa Island and the places around Shangri-La Hotel and the St. Regis Hotel where Trump and Kim are expected to stay, respectively. It heralded the summit as part of a "changed era". After their initial greeting, the leaders will head into a room for the summit.
It's unclear what Trump and Kim might decide Tuesday.
Most observers predicted that the outcome would be a short and vague statement build around the ambiguous aim of the "denuclearisation of the Korean peninsula" leaving it to later bilateral meetings to negotiate what that would mean in practice. He told Lee: "We've got very interesting meeting in particular tomorrow, and I just think it's going to work out very nicely".