The agreement includes a pledge from Kim Jong-un to rid the Korean peninsula of nuclear weapons.
However, in an extraordinary media conference later, President Trump announced details not in the paper.
The American president said he would halt US military exercises in South Korea, something widely seen as a concession.
The Singapore meeting was the first time a sitting US president has met North Korea’s leader, and caps a remarkable turnaround for the two.
For both leaders the meeting brought much to gain as well as considerable risk.
The meeting is seen by North Korea as a way of bringing legitimacy to a nation long regarded as a pariah.
The summit centered on nuclear disarmament and reducing tensions.
The agreement said the US and North Korea would co-operate towards “new relations”, while the US would provide “security guarantees” to North Korea.
On nuclear weapons, Kim Jong-un “reaffirmed his firm and unwavering commitment to complete denuclearization of the Korean peninsula”.
Observers say the document lacks substance, in particular on how denuclearization would be achieved.
Speaking to reporters, President Donald Trump revealed:
Several reporters asked whether President Trump had raised the issue of human rights with Kim Jong-un, who runs a totalitarian regime with extreme censorship and forced-labor camps.
President Trump said he had, and did not retract his description of Kim Jong-un as “talented”.
He said: “Well, he is very talented.
“Anybody that takes over a situation like he did at 26 years of age and is able to run it and run it tough. I don’t say he was nice.”
In a post-summit interview with ABC News, President Trump said he was confident that the agreement meant full denuclearization.
“Yeah, he’s de-nuking, I mean he’s de-nuking the whole place. It’s going to start very quickly. I think he’s going to start now,” he said.
“I think he trusts me and I trust him,” the president added.
Sitting alongside each other, ahead of a one-on-one meeting, President Trump and Kim Jong-un appeared relaxed against the odds.
Kim Jong-un said: “It was not easy to get here.
“There were obstacles but we overcame them to be here.”
The two leaders, accompanied only by interpreters, spoke for a little under 40 minutes. They were then joined by small delegations of advisers for a working lunch.
Over lunch Donald Trump and Kim Jong-un shared a mix of Western and Korean dishes, including stuffed cucumbers and Daegu jorim, a soy-braised fish dish.
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