Trump also agreed to halt joint military exercises between the US and South Korea on the Korean Peninsula, though that decision seemed to surprise both Seoul and the Pentagon. Trump has been talking about that privately for years.
Trump said at a post-summit news conference that he has held off from imposing additional sanctions, but that the United States would life existing ones when the North's nuclear weapons "are no longer a factor".
Current and former USA defence officials expressed concern at the possibility that the United States would unilaterally halt military exercises without an explicit concession from North Korea that lowers the threat from Pyongyang.
But, he acknowledged, "Today is the beginning of an arduous process". North Korea also insists that the USA troop presence in the South, as well as its nuclear "umbrella" over allies Seoul and Tokyo, are part of America's "hostile" policy toward the North. You know, we did sanctions and all the things you would do but I think without the rhetoric, you know, other administrations, I don't want to get specific on that, but you know they had a policy of silence.
"Otto did not die in vain", he said.
"We appreciate President Trump's recent comments about our family", they said.
After hours of discussions, the two men signed an agreement committing the United States to unspecified "security guarantees" in exchange for a denuclearized Korean peninsula. It did not include an agreement to take steps toward ending the technical state of warfare between the USA and North Korea.
After the summit, Cardinal Andrew Yeom Soo-jung of Seoul, South Korea, and apostolic administrator of Pyeongyang, North Korea, celebrated Mass in Myeongdong Cathedral to pray for prompt execution of the summit agreement.More news: Oil edges up, but bulls remain wary ahead of OPEC meeting
Trump challenged criticism of his vague joint statement with Kim.
Trump last month withdrew from the deal, terming it as the "decaying and rotten" agreement.
The formal document signing followed a series of meetings at a luxury Singapore resort.
"Trump loves to characterize things as winners and losers, and Xi Jinping appears to be the biggest victor of all after the historic Trump-Kim summit", said Theresa Fallon, director of the Centre for Russia Europe Asia Studies.
Singapore spent close to $15m to cover the North Korean leader's accommodation, logistics of the meetings, as well as overall security of the two world leaders. Colorado Sen. Corey Gardner said Pence told them that small-scale exercises would continue, but "war games will not".
At stake is not only Kim's regime survival, but also the welfare of his people, who are desperate for greater economic engagement with the world. He set up an emergency meeting with Kim. "They are going to be getting rid of sites". So we look nice and handsome and thin?
One South Korean official said he initially thought Trump had misspoken.
A confident leader strode into the Singapore summit and won. Kim has been accused of horrific rights abuses against his people.