The formal document signing followed a series of meetings at a luxury Singapore resort.
When asked about the video montage played ahead of the press conference, Trump said: "We had it made". Responding to questions, he said "absolutely" he would invite Kim to the White House.
"You see that whenever they're exploding their cannons into the ocean".
Kim and Trump started their first summit with a historic handshake before a row of the national flags of the two countries that lasted for several seconds.
As it turned out, that wouldn't be the end of Trump's casual comments regarding the historical meeting.
Members of the North Korean dictator's entourage will also be present.
Kim, dressed in a dark suit, and Trump, sporting a red tie, talked in a corner of the hotel corridor for a few minutes before they walked along the passage into the meeting room and sat down in front of journalists.
Speaking at a press conference after the signing, President Trump also suggested the US would suspend its joint-military exercises with South Korea in exchange for denuclearization, calling them "very provocative". A buoyant Trump then addresses the photographers, saying: "Getting a good picture everybody - so we all look nice, handsome and thin and flawless".More news: Domino’s now paving potholes to protect pizzas
Then they dined on beef short rib confit along with sweet and sour crispy pork.
Mr Trump and Mr Kim reached a broad agreement that North Korea would move toward denuclearising the Korean peninsula, while the United States committed to providing security guarantees and suspending military exercises with long-time ally South Korea.
U.S. President Donald Trump shakes hands with North Korea's leader Kim Jong Un at the Capella Hotel on Sentosa island in Singapore on June 12, 2018. Kim has been accused of horrific rights abuses against his people.
Little is known about Kim Jong Un's limo but the mass murderer has been fond of the Mercedes S-Class. But he added "our hostages" are back home and testing, research and launches have stopped.
'So I said, "Boy, look at that beach". He also said the US will stop military exercises with South Korea and said eventually the USA could pull troops out of the region completely. Trump left that summit early and, as he flew to Singapore, tweeted that he was yanking the US out of the group's traditional closing statement.
On the US side, President Trump will be accompanied by Pompeo, Bolton, White House Press Secretary Sarah Sanders, ambassador to the Philippines Sung Kim, and Deputy Assistant to the President for Asian Affairs Matthew Pottinger.
Such a meeting was unthinkable even six months ago when the two leaders found themselves in the middle of a verbal confrontation over North Korea's nuclear programme.