"Excitement in the air!" he wrote in a tweet.
Asked about the likely departure times of both leaders, a Singaporean source involved in planning the summit would only say that the host city had factored in the "fluidity of the situation" and was prepared for last-minute changes in the schedule of both leaders.
A jet carrying Kim landed hours earlier.
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.
The two sides met to narrow differences ahead of Tuesday's summit between Trump and Kim, at which the two leaders will discuss efforts to denuclearize the Korean peninsula.
"The entire world is watching the historic summit between (North Korea) and the United States of America, and thanks to your honest efforts. we were able to complete the preparations for the historic summit", Kim told Lee through an interpreter.
On Wednesday, the summit was declared an "Enhanced Security Special Event" by the Minister for Home Affairs under the Public Order Act. U.S. officials were quoted as saying that the two leaders could spend the first two hours alone with translators but not advisors. The official was not authorized to speak publicly about internal deliberations and insisted on anonymity.
One analyst told Al Jazeera Trump will seek to promote his image as a deal-maker.
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Meanwhile, U.S. and North Korean officials huddled at the Ritz-Carlton hotel Monday ahead of the sit-down aimed at resolving a standoff over Pyongyang's nuclear arsenal.
"The entire world is focusing on the historic summit between the DPRK (North Korea) and the U.S., and thanks to your honest efforts".
Trump was joined at the meeting with Lee by US officials including Secretary of State Mike Pompeo, White House Chief of Staff John Kelly and National Security Adviser John Bolton.
The North Korean autocrat's every move will be followed by 3,000 journalists who have converged on Singapore, and by gawkers around the world, up until he shakes hands with Trump on Tuesday.
Trump said after a meeting with North Korean envoy Kim Yong-chul at the Whitehouse.
Outside the Istana, the presidential palace where Trump met Singaporean Prime Minister Lee Hsien Loong, well-wishers displayed American flags and a boy held up a sign reading: "I love President Trump!" He has only publicly left his country three times since taking power after his father's death in late 2011 - traveling twice to China and once across his shared border with the South to the southern part of the Demilitarised Zone for recent summits with the leaders of China and South Korea, respectively.
Trump is expected to meet Lee on Monday.
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.
It also offered a list of Pyongyang's talking points, saying Kim and Trump will exchange "wide-ranging and profound views" on establishing a new relationship, the issue of building a "permanent and durable peace mechanism" and realizing the denuclearization of the Korean Peninsula.
The previous U.S. stance, said Bruce Klingner of the Heritage Foundation, was that "we don't deploy a president to negotiate a treaty, we deploy a president to sign a treaty where we know where every piece of punctuation is on that piece of paper".