Trump told Lee that "we appreciate your hospitality and professionalism and your friendship". "Thank you very much".
The White House released the update Monday morning while announcing the rest of President Trump's schedule.
The U.S. president also dangled the prospect of inviting Kim to Washington if the meeting is a success. He is turning 72 on June 14.
The North Korean leader shook hands with Singaporean Foreign Minister Vivian Balakrishnan shortly after arriving at Singapore's Chagi airport. The meeting was Trump's only scheduled public event today.
"Great to be in Singapore, excitement in the air!" The two men are set to meet for a historic summit on Tuesday where they will focus on the denuclearization of the Korean Peninsula in exchange for the easing of both economic and diplomatic sanctions.
The United States-North Korea summit will likely have significant ramifications on the Korean peninsula and the region; Greg Palkot reports.
During the flight from Canada to Singapore, the president spent time meeting with his staff, reading materials, and preparing for his meetings in Singapore.
"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.
The talks come after a year of surging tensions between the two nuclear-armed rivals that saw Kim ramp up the development of his weapons programs as the two leaders traded a series of pointed personal barbs - as well as threats of war - at one another. Last week, Trump expressed his hope for the normalization of relations with Pyongyang following the summit and did not rule out the signing of a peace treaty between the two countries.
The fighting ended on July 27, 1953, but the war technically continues today because instead of a difficult-to-negotiate peace treaty, military officers for the US -led United Nations, North Korea and China signed an armistice that halted the fighting.