In addition to showing his readiness to shut down the nuclear complex in Yongbyon in the country's northwest, Kim pledged to permanently close North Korea's key missile test site in Tongchang-ri in the presence of global experts.
South Korean officials line up to shake hands with Kim Yong-nam, North Korea's perpetual titular head of state, in Pyongyang on Tuesday.
A range of positive inter-Korean initiatives were also announced on the second day of the Inter-Korean summit in Pyongyang, North Korea's capital.
The South Korean president, Moon Jae-in, can be well satisfied with his third face-to-face meeting with Kim Jong-un in Pyongyang this week, which has brought relations between the two countries to their closest and warmest since the end of the Korean War.
Kim and Moon earlier smiled and chatted as they walked down a hallway and into a meeting room to finalize the joint statement, which also said that the leaders would push for a Korean Peninsula without nuclear weapons and to "eliminate all the danger of war".
Moon said the visit was expected to take place by the end of the year.
But North Korea's packaging of the first images of Moon's visit to its capital this week, as broadcast on state television a full day after the rest of the world saw them, offers some guidance - and some important insight. Two of the previous inter-Korean summits were held in Pyongyang; the other two were held in Panmunjom, the inter-Korean truce village in the Demilitarized Zone.
He noted with apparent approval that the latest inter-Korean summit included a proposal for a potential joint North Korean-South Korean bid for the Olympic Games, adding, "We have a lot of very good things going".
Given present relations, the latter would present nearly insurmountable cross-border customs, immigration, communications and transport challenges - but would certainly segue with Moon's publicly declared hopes of linking the Northern and Southern cross-border road and rail networks. That would give the Koreas until 2025 to put together a joint bid.
Later, Moon, who has fervently pursued engagement with the North, made history by addressing an audience of 150,000 people at a performance of the "mass games", North Korea's synchronized gymnastics and dance show.
As a first step, the North wants the United States to declare an end to the 1950-53 Korean War. Hostilities ceased with an armistice agreement signed on July 27, 1953, by the U.N. Command, North Korea's military and Chinese armed forces.
In Pyongyang, Kim focused on relations with South Korea.
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Didn't Kim already promise to denuclearize?
"Kim Jong Un has agreed to allow Nuclear inspections, subject to final negotiations, and to permanently dismantle a test site and launch pad in the presence of worldwide experts", Trump said in a tweet on Tuesday night.
Shortly after the announcement, Trump called Wednesday's developments "very exciting" on Twitter.
Kim has previously committed to working toward denuclearization, in joint statements with both Moon and Trump.
In Singapore, Kim declared his backing for the denuclearisation of the peninsula, but no details were agreed and Washington and Pyongyang have since sparred over what that means and how it will be achieved.
"In the meantime there will be no Rocket or Nuclear testing", Mr Trump said in a pair of tweets.
Yoon, South Korea's presidential senior secretary for public communications, said Moon's visit on Wednesday afternoon had been previously scheduled and "simply consists of viewing artworks".
Experts warn that such a process will take years, and will be extremely invasive.
"But it is no closer to North Korean disarmament", he said.
Residents of Pyongyang, North Korea gather in a plaza outside the city's main train station to watch the news of South Korean President Moon Jae-in's visit on Wednesday, Sept. 18, 2018.
During April's first summit with Moon, Kim said he wanted to invite Moon to the North but that he was "concerned that our transportation (infrastructure) is inadequate". "Obviously, much depends on the American reaction, but looking at Trump's tweeted response, we're on course".
Moon also said he expected the immediate beginning of cooperation in the area of health and welfare to prevent the spread of contagious diseases across the border.