Trump traveled to Singapore from Canada, where he attended a meeting with other world leaders.
A jet carrying Kim landed hours earlier. On Monday, she met senior USA diplomat Sung Kim at the Ritz-Carlton hotel to make final preparations for the summit.
A Trump administration official, speaking on condition of anonymity, said the US side was entering the talks with a sense of optimism and an equal dose of skepticism given North Korea's long history of developing nuclear weapons.
In part, these lowered expectations are a reflection of the extreme skepticism among many that the North can be persuaded to give up a nuclear programme it has stubbornly built over the decades, often in secrecy and despite intense sanctions, global condemnation and widespread suffering among its people.
Kim smiled broadly Sunday evening as he met with Singapore Prime Minister Lee Hsien Loong.
Trump spoke only briefly in public on Monday, forecasting a "nice" outcome.
North Korea has previously said it was willing to discuss denuclearization, but experts have expressed concern over the varying definitions of the term held by Washington and Pyongyang. The official was not authorized to speak publicly about internal deliberations and insisted on anonymity. In some instances, past deals struck by previous USA administrations with North Korea paused - but failed to roll back - North Korea's program, which has only grown over the years. It also has two presidential suites, so Trump and Kim won't have to duke it out over who gets the big room.
The MFA also said Lee will meet President Trump separately on Monday. Add North Korea as an interest to stay up to date on the latest North Korea news, video, and analysis from ABC News.
AFP 2018 Saul Loeb World Follows Every Step of Historic Trump Kim Summit
USA and North Korean officials are set to meet Monday morning in Singapore to make final preparations for Tuesday's meeting.
After a sudden and welcome turn to diplomacy following last year's threats, insults and fears of war - remember "fire and fury" and "dotard"?
President Trump shakes hands with North Korea leader Kim Jong Un at the Capella resort on Sentosa Island in Singapore on Tuesday. One dispatch by the Korean Central News Agency said North Korea and the United States would exchange "wide-ranging and profound views" on establishing new relations, building a "permanent and durable peace-keeping mechanism", achieving denuclearization and "other issues of mutual concern, as required by the changed era".
Part of the interest in Tuesday's summit is simply because Kim has had limited appearances on the world stage.
"Thanks PM Lee for spending $20 million of taxpayers money, which can. help a lot of needy families in Singapore to survive", posted one Facebook user.
There was speculation throughout the day over whether Kim Jong Un had taken his private jet- an Ilyushin IL-62M - from Pyongyang, but official photos released by the Singaporean Ministry of Communications and Information showing Kim meeting Balakrishnan on the tarmac appear to reveal that he flew to Singapore aboard an Air China Boeing 747.
Trump initially touted the potential for a grand bargain with North Korea to rid itself of a nuclear missile program that has advanced rapidly to threaten the United States.
"While a summit between Trump and Kim would be historic, it is unlikely to be decisive".