A jet carrying Kim landed hours earlier.
Pompeo also expressed confidence of a "successful outcome" but said that the summit would also lead to a lot more to be done in the path ahead, providing a "framework for the hard work that will follow". The talks are expected to be devoted to the future of Pyongyang's nuclear program and the lifting of economic sanctions.
Mr Kim was sent off in a ceremony at the Pyongyang airport joined by a group of senior officials, such as Mr Kim Yong Nam, the North's nominal head of state, Mr Choe Ryong Hae, vice-chairman of the North's State Affairs Commission, and Prime Minister Pak Pong Ju.
Cheering crowds greeted Kim during his stroll, and cameras from North Korea's state-run Korean Central News Agency documented his every move.
Trump is set to meet with Lee on Monday.
The meeting marks the first ever meeting between a sitting North Korean leader and a USA president. She previously worked as an English-language interpreter for a North Korean delegation attending now-stalled six-nation nuclear disarmament talks. North Korea also wants an end to what it considers America's "hostile policy" and a security guarantee that the US will not seek to remove the regime.
AFP 2018 Saul Loeb World Follows Every Step of Historic Trump Kim Summit
It was not immediately clear what specific progress, if any, had been made in preliminary discussions between USA and North Korean officials.
The United States is prepared to provide North Korea "unique" security guarantees if it undertakes "complete verifiable and irreversible" denuclearisation, Secretary of State Michael Pompeo said on Monday.
Trump arrived at the hotel after issuing a flurry of tweets dismissing skeptics of the meeting between USA leaders and the rogue nuclear nation as "haters & losers". It's a reflection of the intense global curiosity over Kim's sudden turn to diplomacy in recent months after a slew of North Korean nuclear and missile tests past year raised serious fears of war.
In March, Trump accepted Kim's invitation to meet, breaking with predecessors who had shunned any type of a summit without major concessions from North Korea or multilateral talks that included a host of other Asian countries. It heralded the summit as part of a "changed era".
It's Kim's pursuit of nuclear weapons that gives his meeting with Trump such high stakes.
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.
The summit has officially begun, with Trump and Kim shaking hands and posing for photographs. China and South Korea would have to sign off on any legal treaty. Meanwhile, Mr Kim has called Mr Trump "mentally deranged" and a "dotard".
The meeting would have been unthinkable a year ago when tensions spiraled in the region over North Korea's nuclear and missile programs as it raced toward the goal of developing a nuclear-tipped missile capable of hitting the United States.