Just meeting with Trump will also give Kim a recognition North Korea has long sought, setting him up as global player and equal to the US domestically and, internationally, as the leader of a "normal country" worthy of respect.
At 10am, North Korean vice-minister for foreign affairs, Choi Sun-hee, strode into the Ritz Carlton with her small team.
For the North, Kim Jong Un has already won a huge propaganda bonus by merely having the summit and sitting down as an equal with the USA president, an accomplishment his father and grandfather sought but could never realize.
The North Korean motorcade drives out from Singapore's Changi Airport after Kim Jong Un's arrival in the city-state.
Officials who arrived with Trump include Secretary of State Mike Pompeo, National Security Adviser John Bolton, White House Chief of Staff John Kelly and White House Press Secretary Sarah Sanders.
"The entire world is watching the historic summit between the DPRK (North Korea) and the United States of America", Kim told Lee, using his country's official name, the Democratic People's Republic of Korea.
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Just meeting with Mr Trump will also give Mr Kim recognition as the leader of a "normal" country and as an equal of the USA leader.
Enemies since the 1950-53 Korean War, the leaders of North Korea and the United States have never met previously - or even spoken on the phone.
President Trump is expected to meet separately with Singapore Prime Minister Lee Hsien Loong on Monday. While Kim and his delegation are now staying at the St. Regis Hotel amid heavy security.
Nuclear negotiators representing North Korea and the US have another busy hours ahead of them.as they sit down for another round of talks to fine-tune the agenda for tomorrow's highly-anticipated summit.
When pressed for a breakdown on the summit expenses, he said, "I think if you calculate the price of everything in this world, you will miss out the really important things".
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Kim smiled broadly Sunday evening as he met with Singapore Prime Minister Lee Hsien Loong. "It will certainly be an exciting day and I know that Kim Jong-un will work very hard to do something that has rarely been done before".
It will be the first ever meeting between a sitting US President and North Korean leader.
Air Force One touched down at a military air base, travelling from Canada, where Trump had attended a meeting of the Group of Seven nations.
In a statement released by the state news agency KCNA, it said the two leaders would discuss a "permanent and durable peace-keeping mechanism" for the Korean Peninsula, the "denuclearisation" of the Korean peninsula and other issues of mutual concern.
Mr Trump could also consider opening an American embassy in Pyongyang, the report said.
Both countries want North Korea's nuclear capabilities addressed.
Lee suggested that Singapore ― one of the few countries that has diplomatic relations with both Washington and Pyongyang ― also could benefit from the meeting thanks to the "publicity" generated about the Southeast Asian island.
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