The North will also permanently dismantle its Nyongbyon nuclear complex so long as the United States takes corresponding measures.
As a next step, North Korea will allow experts from "concerned countries" to watch the closure of its missile engine testing site and launch pad in the northwestern town of Dongchang-ri, according to a joint statement signed by Moon and Kim.
The North Korean leader would likely visit Seoul later this year, Mr Moon said.
Wednesday's talks took place at the Paekhwawon official guest house on the outskirts of Pyongyang.
Still, the offers suggests that South Korean President Moon Jae-in has struck, if not gold, then certainly silver, in his aim of getting the stalled denuclearization process, on which North Korea and the United States are deeply divided, back on track.
A big part of any negotiation to end the war would be the status of the thousands of U.S. troops stationed in South Korea as part of the two countries' alliance.
Experts in Seoul say that the two leaders' visit to the mountain would be an indication that the two Koreas believe they held a successful summit, with progress in inter-Korean ties.
Water will haunt Carolinas after Florence — WHAT'S HAPPENING
The flooding is coming from rivers, rather than the ocean, thanks to the feet of rain that have fallen since Thursday night. On Tuesday, the storm's remnants were continuing to soak the mid-Atlantic region and southern New England with heavy rain.
Trump was enthusiastic about the summit, declaring that Kim "has agreed to allow Nuclear inspections, subject to final negotiations". Such a trip would be the first by any North Korean leader, another dramatic moment in the flurry of diplomacy around the North's nuclear weapons program in recent months.
North Korea's participation in hosting the Games, which include thousands of athletes from around the world and an even larger number of spectators, would be a watershed event requiring a degree of openness and financial muscle now lacking in the isolated and impoverished country.
Paektusan has taken on mythological status in North Korea, with North Korean history being rewritten to claim Kim's father - Kim Jong-il - was born on the mountain.
US State Department spokeswoman Heather Nauert stated on Tuesday that Washington hopes the latest inter-Korean summit will bring about "meaningful, verifiable steps towards the denuclearisation of North Korea" and branded it a "historic opportunity".
The two Koreas agreed to begin construction to reconnect railways and roads linking the countries within this year.
In their third summit, Kim and Moon also laid out plans to draw down forces along their heavily fortified border and announced an agreement for their athletes to compete as a single team at the 2020 Olympics in Tokyo and to submit a joint bid to host the games in 2032.
The leaders agreed to set up a buffer zone in the Yellow Sea to suspend firing of guns and maritime drills, as well as a no-fly zone in border areas to prevent accidental plane clashes.
The North's unique brand of choreographed mass adulation was on full display as hundreds of people waved North Korean flags and another depicting an undivided peninsula - while the South's own emblem was only visible on Moon's Boeing 747 aircraft.
Moon and ministers were not the only South Koreans in Pyongyang on Wednesday.