The two leaders met on Tuesday, signing a brief declaration on denuclearisation and reducing tensions.
President Donald Trump said afterwards that sanctions would remain in place for now, but would be lifted once "nukes are no longer a factor".
He also announced an unexpected end to US-South Korea military drills.
The move - long demanded by Pyongyang - has been seen as a major concession to North Korea and appeared to take US allies in the region by surprise.
The Pentagon has since sought to reassure its allies of its "ironclad" security commitments.
North Korea's media is tightly controlled by the government and only ever reports positively on officials' activities. It rarely reports on leader Kim Jong-un's activities in real time
But Tuesday's summit in Singapore was front page news on Wednesday, with multiple images of Mr Kim alongside Mr Trump.
Official newspaper Rodong Sinmun called the summit "the meeting of the century" on its front page.
State media agency KCNA published an enthusiastic article in English praising the talks as a historic break from the past.
The declaration signed at the end of the summit said the two countries would co-operate towards "new relations", while the US would provide "security guarantees" to North Korea
Pyongyang in return "commits to work toward complete denuclearisation of the Korean peninsula," the document says.
Most Western observers have said the deal appears to include significant concessions from the US while including no new commitments from North Korea nor details on how denuclearisation could be achieved.
KCNA has focused on those elements as a great breakthrough for North Korea
"Trump expressed his intention to halt US-South Korea joint military exercises, offer security guarantees to the North and lift sanctions against it along with advance in improving the mutual relationship through dialogue and negotiation," it said.
Although not part of the joint declaration, Mr Trump said after the summit that sanctions "will come off" once the US is sure that the nukes are no longer a factor". He also said he hoped that this would be soon.
Depicting the two leaders very much as equals at the meeting, KCNA quotes Mr Kim as saying it was urgent "to make bold decision on halting irritating and hostile military actions against each other".
KCNA also reported that both leaders had agreed to visit each other in the US and North Korea respectively.