Speaking about Kim, Trump said "we have developed a very special bond" and is "absolutely" willing to invite Kim to the White House.
Arriving at the Prime Minister's office after 1900 local time, Kim shook hands with Lee and his staff then sat down to begin talks in front of the cameras before the press was ushered out a few minutes later.
Both leaders expressed optimism throughout roughly five hours of talks, with Trump thanking Kim afterward "for taking the first bold step toward a bright new future for his people".
Trump and Kim shook hands and posed for photos before their almost 40-minute one-on-one conversation behind closed doors.
The document signing followed a series of meetings at a luxury Singapore resort.
The two leaders will likely have to conduct reciprocal visits to each other's capitals over coming years before hatching out a final deal.
Emery wants Sokratis and Fellaini at Arsenal
However, Jurgen Klopp is ready to let Salah go, as reports claim that he has already found a replacement for him in Nabil Fekir. Barcelona forward Lionel Messi has backed the club's pursuit of Atletico Madrid striker Antoine Griezmann .
Kim stood silently alongside Trump as he spoke to media during a post-lunch stroll through the gardens of the Singapore hotel where the summit was held, but the North Korean leader had earlier described their meeting as a "a good prelude to peace".
Kim spoke at the signing, through a translator, saying that they had a "historic meeting and made a decision to leave the past behind". "Did Kim Jong-un just make a vague Iron Sky reference?" Since 1953, a ceasefire has made that conflict largely symbolic, with suffering limited to South Koreans killed in provocative strikes, and the North Koreans who suffer in a gulag state or die fleeing it.
For his part, South Korean President Moon Jae-in said on Monday that he hopes Trump and Kim "generously" consider each other's demands and meet the people's wish for a new era for the Korean Peninsula.
The North Korean leader, however, provided Trump a chance for diplomatic redemption, no matter how fleeting.
Aware that the eyes of the world were on a moment many people never expected to see, Kim said many of those watching would think it was a scene from a "science fiction movie".
Graham, who called the "comprehensive" document Mr. Trump and Kim signed on Tuesday an "agreement in principle", said the end of the military exercises with South Korea gives the U.S.
However, Leong said both found it hard to hide their nervousness once they were seated, with Trump displaying a slanted smile, and fidgeting with his hands and Kim leaning and staring at the ground.
The former National Basketball Association star was in Singapore for the summit, although the White House has repeatedly said he's not an official part of the USA delegation. We'll be doing something on it.