The US president described the North Korean leader as a “very talented” negotiator and said their meeting was “honest, direct and productive”.
He provided security guarantees for Pyongyang and in return expects the process of denuclearisation to be started “very, very quickly”.
He insisted it would be verified – but critics will say the commitment amounts to nothing new.
“Anyone can make war but only the most courageous can make peace,” Mr Trump said in a news conference after the talks.
In an interview given afterwards too, he defended the harsh language he used before relations between the US and North Korea began to thaw.
He has called Mr Kim “little rocket man” and threatened “fire and fury”.
But he told Fox News: “I think without the rhetoric we wouldn’t have been here.”
He tweeted: “Great progress was made on the denuclearisation of North Korea.
“Hostages are back home, will be getting the remains of our great heroes back to their families, no missiles shot, no research happening, sites closing.
“Got along great with Kim Jong Un who wants to see wonderful things for his country. As I said earlier today: Anyone can make war, but only the most courageous can make peace!”
The two leaders posed for a 13-second handshake before talks began – with their body language the subject of much analysis throughout the morning.
They later enjoyed a lunch that included a traditional prawn cocktail, fresh octopus, beef short rib confit with potato dauphinoise, soy braised codfish and Häagen-Dazs vanilla ice cream with cherry coulis.
During the summit, Mr Kim was shown a White House-produced video about a vision for North Korea without nuclear weapons.
The US government made it to help persuade the dictator to do a deal, a White House official said.
Following the meeting, Mr Kim said the US and North Korea had “decided to leave the past behind” and that the world would see a “major change”.
In a joint statement released by the White House, the two leaders said they had conducted a “comprehensive, in-depth, and sincere exchange of opinions” on issues related to the “building of a lasting and robust peace regime on the Korean Peninsula”.
Mr Trump committed to provide “security guarantees” to North Korea, while Mr Kim “reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean Peninsula”, the statement said.
The US president told reporters that Mr Kim had agreed North Korea would destroy a major engine-testing site used for missiles.
Mr Trump also said America’s joint military exercises with South Korea would be halted and would not be revived “unless and until we see the future negotiation is not going along like it should”.
And he revealed he would visit Pyongyang “at a certain time” and that he had invited Mr Kim to the White House.
However, Mr Trump said sanctions would remain in effect until denuclearisation happened, and there would be no reduction in the US’s military presence in the region.
Asked by reporters if he raised human rights issues with Mr Kim, the president replied they had talked about the issue “briefly”.
Mr Trump was also challenged by a reporter about calling Mr Kim as “very talented”. The president defended his description, saying he had not called his counterpart “nice”.
Reaction has been mixed. The Democrats’ leader in the Senate, Charles Schumer, said President Trump had given up some American leverage over North Korea.
Describing the get together as a “reality show summit”, Mr Schumer said the “meeting alone will be a victory for North Korea and a defeat for the US”.
But UN secretary general Antonio Guterres called the summit “an important milestone” in advancing peace and “complete and verifiable denuclearisation on the Korean Peninsula”.
Earlier, the president hailed the meeting as “better than anybody expected” and, after one-to-one talks and a working lunch, the pair strolled around the five-star Capella Hotel in Singapore, smiling and chatting.
Mr Trump also showed Mr Kim the interior of his limousine and told reporters: “It’s going great.”
Through an interpreter, North Korea’s leader said: “The road leading up to here was not that smooth. We’ve overcome so many obstacles which blocked our eyes and ears, dragging our feet down due to the past history, prejudices. But despite of all that, we’ve made it here.”
Mr Kim was heard telling the US president: “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.”
The two leaders talked alone for about 40 minutes and were joined only by interpreters – a move that retired US officials said posed an “unacceptable threat”.
They then proceeded to a larger meeting along with officials from their delegations.
Sitting across from Mr Kim and his team at the larger meeting was the US leader, his chief of staff John Kelly, secretary of state Mike Pompeo and national security adviser John Bolton.
At the start of a meeting seeking ways to end a nuclear stand-off on the Korean peninsula, Mr Trump told the North Korean leader: “Working together we will get it taken care of… we will solve it.”
Reacting to the news of the two leaders meeting, basketball star and unlikely North Korea envoy Dennis Rodman, who is also in Singapore, said holding the summit was the right thing to do.
He told CNN: “We need the doors to be open and start fresh and make this world a better place, baby, that’s it.”
He also broke down in tears live on television as he spoke about the hostility he faced for previously meeting Mr Kim, who he struck up a friendship with over their love of basketball. The former NBA player has visited Pyongyang five times since the North Korean leader took charge.
Before the meeting, Mr Trump predicted he might strike a deal with Mr Kim over nuclear weapons or officially bring the Korean War to an end.
However, the US leader’s short stay in Singapore has raised questions over whether his ambitions have been scaled back.