There were mo immediate details on the contents of the document.
Although the breakthrough made at the summit marks just the start of a diplomatic process, it could bring lasting change to the security landscape of Northeast Asia, just as former U.S. President Richard Nixon visit to Beijing in 1972 led to the transformation of China.
Before signing what Trump described as a “comprehensive letter”, Kim said the two leaders had a historic meeting “and decided to leave the past behind. The world will see a major change.”
Trump said the process of denuclearization would happen “very, very quickly”, adding that he had formed a “special bond” with Kim and the relationship with North Korea would be very different.
“This is going to lead to more and more and more,” Trump said.
Asked whether he would invite Kim to the White House, Trump said: “Absolutely, I will.”
During a post-lunch stroll through the gardens of the Singapore hotel where the summit was held, Trump said the summit had gone “better than anybody could have expected”.
Kim stood silently alongside, but the North Korean leader had earlier described their meeting as a “a good prelude to peace”.
Both men walked to Trump’s bullet-proof limousine, nicknamed “The Beast”, and looked in at the rear seat, with Trump apparently showing Kim something inside. They then resumed their walk.
Both men had appeared cautious and serious when they first arrived for the summit at the Capella hotel on Singapore’s Sentosa, a resort island with luxury hotels, a casino, manmade beaches and a Universal Studios theme park.
But, with cameras of the world’s press trained on them, they displayed an initial atmosphere of bonhomie as they met on the verandah of the Capella, a refurbished 19th century British regimental officers’ mess.
After a handshake, they were soon smiling and holding each other by the arm, before Trump guided Kim to the library where they held a meeting with only their interpreters. Trump had said on Saturday he would know within a minute of meeting Kim whether he would reach a deal.
Inside, they sat alongside each other against a backdrop of North Korean and U.S. flags, with Kim beaming broadly as the U.S. president gave him a thumbs up.
The combatants of the 1950-53 Korean War are technically still at war, as the conflict, in which millions of people died, was concluded only with a truce.
After initial exchanges lasting around 40 minutes, Trump and Kim emerged, walking side-by-side through the colonnaded hotel before entering a meeting room, where they were joined by their most senior officials.
Kim was heard telling Trump through a translator: “I think the entire world is watching this moment. Many people in the world will think of this as a scene from a fantasy...science fiction movie.”
Asked by a reporter how the meeting was going, Trump said: “Very good. Very, very good. Good relationship.”
Kim also sounded positive about the prospects of peace.
“We overcame all kinds of scepticism and speculations about this summit and I believe that this is good for the peace,” he said. “I believe this is a good prelude for peace.”
The dollar jumped to a 3-week top on Tuesday and Asian shares rose on the news.
Trump was joined by Secretary of State Mike Pompeo, National Security Adviser John Bolton, and John Kelly, White House Chief of Staff, for the expanded talks, while Kim’s team included former military intelligence chief Kim Yong Chol, foreign minister Ri Yong Ho and Ri Su Yong, vice chairman of the ruling Workers’ Party.