Trump also said he wanted to withdraw the USA troops stationed in the South, something he promised on the campaign trail, saying: "I'd like to be able to bring them back home".
Even Kim recognised how freakish a meeting it was; a meeting of equals between the leader of an impoverished rogue nation and the president of the most powerful country in the world.
Both leaders spoke briefly before the doors were shut to the gathered press, with Trump saying that he thought it would be "tremendously successful".
Trump calls Kim "a very talented man", may invite him to the White House.
The signing came after a one on one meeting between Kim and Trump which was followed by an expanded bilateral meeting with their aides and a working lunch.
While the discussions between the two leaders were no doubt serious, people have also been talking about a joke from the President that seemed to fall flat on its feet.
After months of nail-biting anticipation, the United States President Donald Trump held a historic meeting with North Korean leader Kim Jung-un.
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They also have some way to go before matching the likes of Manchester United, who won three Premier League titles in a row twice. The midfielder had to wait until City's final home game of the season against Brighton for his first start of the season.
Kim spoke at the signing, through a translator, saying that they had a "historic meeting and chose to leave the past behind".
The North Korean leader then traveled to the St. Regis Hotel - where he will be staying for the duration of the visit - in his armored limousine, which arrived on a separate flight. South Korea contributes, but not 100 percent, which is a subject that we have to talk to them about also.
A South Korean official said he initially thought Trump had misspoken.
"We hope the summit will be a success and bring us a complete denuclearisation, peace and a new era" in relations between the two Koreas and the United States, South Korean President Moon Jae-in said.
The media spotted Trump and Kim approaching the limousine, adorned with an American flag. "Many people in the world will think of this as a scene from a fantasy.science fiction movie".
Before getting on a plane headed back to the U.S., Trump held an hour-long press conference with the gathered global media, describing his hopes for the impact of the summit.
Former professor, Michel Riesen (top right) who taught Kim when he was around 14-years-old in Switzerland says he would have absolutely learned basic English. We've overcome so many obstacles which blocked our eyes and ears, dragging our feet down due to the past history, prejudices. We'll be doing something on it.