The nuclear discussions had stalled after the first historic summit between Trump and Kim in Singapore in June, when Kim declared his backing for denuclearisation of the peninsula but no details were agreed.
"We have agreed to make the Korean Peninsula a land of peace that is free from nuclear weapons and nuclear threat", Kim said.
The two leaders also agreed to open a permanent facility for family reunions, work towards joining up road and rail links, and bid jointly for the 2032 Olympics.
In a joint statement after the summit with Mr Moon, Mr Kim pledged to permanently abolish North Korea's key missile facilities in the presence of foreign experts. "It is not clear whether Moon got enough to satisfy Trump _ we will find out about that next week", Snyder said in the interview.
A copy of an article of the North's official newspaper Rodong Sinmun dated December 26, 1980 calls Mount Paektu a "sacred mountain of revolution" spearheaded by Kim Il Sung "in the flames of the arduous 20-year anti-Japan struggle".
U.S. President Donald Trump hailed the results of the summit between the leaders of the two Koreas. Kim's offer, however, could provide a way to jump start talks, analysts say.
In the meantime, however, Moon and Kim made concrete moves of their own to reduce tensions on their border.
Many also believe the North has other covert nuclear facilities. "If North Korea is genuinely willing to close down Yongbyon and to allow in inspectors ... those are just partial steps, but those are genuine steps forward", said Michael Fuchs, a senior fellow at the Center for American Progress and former deputy assistant secretary of state for East Asian and Pacific affairs.
Shortly after the announcement, Trump called Wednesday's developments "very exciting" on Twitter.
"I have a dream that I have not been able to fulfil for a long time, which is trekking Mount Paektu", Moon said at the time.
But while Moon's warm reception in the North Korean capital and smiling photo opportunities have already been considered a diplomatic victory, a number of global policy experts are still uncertain as to whether facility shutdowns in Yongbyon will actually cease all nuclear production, with the Times noting that some foreign analysts suspect that Kim has other nuclear programs operating in secret.
Washington has demanded concrete action toward denuclearisation, such as a full disclosure of North Korea's nuclear and missile facilities, before agreeing to key goals of Pyongyang, including an easing of global sanctions and an official end to the Korean War.
However, their deal on the issue most fascinating and worrisome - the North's pursuit of nuclear-tipped missiles that can accurately strike the US mainland - contained a big condition: North Korean leader Kim Jong-un stated he would permanently dismantle his country's main nuclear complex only if the United States takes unspecified corresponding measures. "Chairman Kim and I will rebuild our nation, with 80 million people of the North and South holding hand in hand, standing strong".
It also was unclear what "corresponding steps" North Korea wants from the USA to dismantle its nuclear site.
Even though it was not specified in the agreement signed Wednesday between Moon and Kim, the Sejong Institute's Woo Jung-yeop assumes North Korea means they're looking for a declaration from Washington to formally end the Korean War.
For its part, Pyongyang - which wants a formal declaration the 1950-53 Korean War is over - has condemned demands for its unilateral disarmament as "gangster-like".
Mr Pompeo cited North Korean leader Kim Jong-un's decision to "complete the previously announced dismantlement of the Tongchang-ri site in the presence of USA and global inspectors as a step toward the final fully verified denuclearisation of North Korea".