The US “committed to provide security guarantees” to North Korea, according to an agreement signed by both leaders in Singapore following decades of hostilities between the two nations.
Mr Trump said he expected the denuclearisation process to start “very, very quickly”. US secretary of state Mike Pompeo and North Korean officials will hold follow-up negotiations “at the earliest possible date”, the joint statement said.
However, the document did not give a definition of denuclearisation or details of how it would be achieved.
It also also made no mention of the crippling international sanctions imposed on North Korea as it pursued its nuclear weapons programme.
Nor was there any reference to the signing of a peace treaty. The US and North Korea technically remain in a state of warfare as the 1950-53 Korean War, in which millions of people died, was concluded only with a truce.
But the joint statement did say the two sides had agreed to the recovery and repatriation of the remains of prisoners of war and those missing in action.
If the agreement leads to a lasting easing of hostilities, it could fundamentally change the security landscape of north-east Asia, just as former US president Richard Nixon visit to Beijing in 1972 led to the transformation of China.
Before signing what Mr Trump described as a “comprehensive” document, Mr Kim said the two leaders had a historic meeting “and decided to leave the past behind”.
“The world will see a major change,” the North Korean leader added.
The joint statement contained four bullet-pointed commitments, one of which stressed “efforts to stablish new relations in accordance with the desire of the peoples of the two countries for peace and prosperity”.
The US and North Korea will also “join their efforts to build a lasting and stable peace regime on the Korean Peninsula”, the agreement stated.
The White House has yet to release the document’s text, but it was photographed by the media as Mr Trump displayed it at a signing ceremony at the resort island of Sentosa.
During an after-lunch stroll through the gardens of the hotel where the summit was held, Mr Trump said the meeting had gone “better than anybody could have expected”.
Mr Kim stood silently alongside, but the North Korean leader had earlier described the meeting as a “a good prelude to peace”.
The president said he had formed a “very special bond” with Mr Kim and that the US relationship with North Korea would be very different.
“People are going to be very impressed and people are going to be very happy and we are going to take care of a very dangerous problem for the world,” Mr Trump said
He described Mr Kim “very smart” and a “very worthy, very hard negotiator.”
“I learned he’s a very talented man. I also learned that he loves his country very much,” he added.
Mr Trump had predicted on Saturday he would be know within a minute of meeting the North Korean leader whether they would reach a deal.
They had appeared cautious and serious when they first arrived for the summit at the Capella hotel on Sentosa, a resort island with luxury hotels, a casino, manmade beaches and a Universal Studios theme park.
But, with cameras of the world’s media trained on them, they displayed an initial atmosphere of bonhomie as they met on the hotel’s verandah of the hotel, a refurbished 19th century British regimental officers’ mess.
Body language expert said both men tried to project command as they met, but also displayed signs of nerves.
After a handshake, the leaders were soon smiling and holding each other by the arm, before Mr Trump guided Mr Kim to the library where they held a meeting with only their interpreters.
Inside, they sat alongside each other against a backdrop of North Korean and US flags, with Mr Kim beaming broadly as the president gave him a thumbs up.
After initial exchanges lasting around 40 minutes, the leaders emerged, walking side-by-side through the hotel before entering a meeting room where they were joined by their most senior officials.
Mr Trump was joined by Mr Pompeo, as well as national security adviser John Bolton, and John Kelly, White House chief of staff, for the expanded talks. Mr 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.
In the hours before the summit began, Mr Trump expressed optimism while Mr Pompeo injected a note of caution about whether Mr Kim would prove to be sincere about his willingness to denuclearise.
The secretary of state said the meeting should set the framework for “the hard work that will follow”, insisting that North Korea had to move towards complete, verifiable and irreversible denuclearisation.
Pyongyang, however, has shown little appetite for surrendering nuclear weapons it considers vital to the survival of Mr Kim’s dynastic rule.
Sanctions on North Korea would remain in place until that happened, Mr Pompeo said on Monday.
“If diplomacy does not move in the right direction… those measures will increase,” he added.
The White House said later that discussions with North Korea had moved “more quickly than expected” and Mr Trump would leave Singapore on Tuesday night following the summit, rather than Wednesday, as previously scheduled.
Mr Kim was due to leave on Tuesday afternoon, a source involved in the planning of his visit said.
Mr Trump spoke to South Korean president Moon Jae-in and Japan’s prime minister Shinzo Abe, both key allies of Washington in the region, to discuss developments ahead of the summit.
“I too, got little sleep last night,” Mr Moon told his cabinet in Seoul as the summit began in Singapore. “I truly hope it will be a successful summit that will open a new age for the two Koreas and the United States and bring us complete denuclearisation and peace.”