While the declaration appears to fall short of what the U.S. wants, President Donald Trump has maintained that he and Mr Kim have a good relationship and both leaders have hinted they may meet again, following their June summit in Singapore.
North and South Korea agreed that the Korean Peninsula should turn into a "land of peace without nuclear weapons and nuclear threats", Moon said. "The road to our future will not always be smooth and we may face challenges and trials we can't anticipate".
As a first step, the North wants the United States to declare an end to the 1950-53 Korean War.
The North had agreed to "permanently close" a missile engine testing site and launch facility in Tongchang-ri "in the presence of experts from relevant nations", he added. That is a site he had already promised to close, although allowing in foreign inspectors would be a step forward.
"If my visit helps restart North Korea-US dialogue, that itself will be highly meaningful", Moon said Tuesday.
But there wasn't enough in terms of new, concrete promises to satisfy many experts.
The outcome will also be a litmus test for another meeting Mr Kim has recently proposed to Mr Trump.
And arms control expert Jeffrey Lewis said the consensus view was that its uranium enrichment facility "was built for (the) express objective of being sacrificed", tweeting that he presumed the North had "at least one more" production site.
The North's offer to take additional denuclearization steps despite any signs of reward from the United States is apparently aimed at restarting its denuclearization talks with the US.
The US is pressing countries to strictly observe United Nations sanctions aimed at choking off funding for Pyongyang's nuclear and ballistic missile programmes, which are a threat to the US.
The view from Seoul will largely be relief, mixed with a sort of built-in wariness that many here wield as a default reaction to anything having to do with their northern neighbors.
The signed agreement stated that Kim would travel to Seoul "as soon as possible", something no North Korean leader has ever done.
"If Yongbyon is actually frozen, it will not mean the end of their nuclear program, it will not even mean the end of their production of nuclear weapons, but it will be a significant decline in their ability to produce more nuclear material and nuclear weapons", he said.
The two Koreas also agreed to establish buffer zones along their land and sea borders to reduce military tensions and prevent accidental clashes.
The two leaders also announced plans to bid for a joint hosting of the Olympics, oddly enough.
The Kaesong complex was shut down in early 2016 as part of Seoul's unilateral sanctions against the North.
Kim Yo Jong shares with Kim Jong Un the Baektu bloodline that flows from late North Korean leader Kim Il Sung, which they say legitimizes the Kim dynasty's regime.
President Moon stated his visit could take place within the year, barring unforeseen circumstances.
Kim Yo Jong, North Korean leader's sister, directs the welcoming ceremony for South's delegation at Sunan International Airport, Pyongyang, North Korea, Sept. 18, 2018.