He added that Pyongyang will close its missile testing site and will take additional steps such as closing its main Yongbyon nuclear complex if the United States takes reciprocal measures.
The joint declaration, later released by Seoul's presidential office Cheong Wa Dae, showed the North's agreement on denuclearization steps.
"Hero remains to continue being returned home to the United States".
In previous, failed talks, North Korea said it could consider giving up its nuclear programme if the USA provided security guarantees by removing troops from South Korea and withdrawing its so-called nuclear umbrella of deterrence from the South and Japan.
Afterwards, Moon will attend a performance of the "Mass Games" - North Korea's spectacular, all-dancing propaganda display.
The North has been demanding that Washington join the two Koreas in making a joint declaration ending the Korean War.
Mr Trump has welcomed the result of the outcome of the summit on Twitter already and lauded Kim Jong-un's gesture to leave nuclear-capable missiles out of the 9 September military parade to commemorate the country's 70th founding anniversary.
South Korea's president and the North's leader Kim Jong Un drove together through the streets of Pyongyang on Tuesday past thousands of cheering citizens before opening a summit where Moon Jae-in will seek to reboot stalled denuclearisation talks between his hosts and the United States.
Moon Jae-in might just be able to convince the USA president to give Kim Jong-un another chance with diplomacy.
"It's not too much to say that it's Moon's efforts that arranged a historic North Korea-U.S. summit".
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Still, Moon's top security adviser, Chung Eui-yong, insisted the outcome of the latest inter-Korean summit will lead to a resumption of U.S.
Importantly, North Korea has completed development work on its large liquid propellant engines for intercontinental-range ballistic missiles. Moon said the visit was expected to take place by the end of the year.
Moon said Kim's visit to Seoul could happen this year and would be a "turning point in South-North relations". Kim called the agreement "a leap forward" toward peace between the two historically bitter rivals.
The two Koreas agreed to begin construction to reconnect railways and roads linking the countries within this year.
According to the spokesman, they will take a flight from Sunan International Airport to Samjiyon Airport near the mountain and ride a bus to a stop halfway up the mountain, before switching to a track vehicle to reach the peak. The first goal still looks far more realistic than the second. The signed agreement stated that Kim would travel to Seoul "as soon as possible", something no North Korean leader has ever done.
This will include "all artillery drills and field training exercises at the regiment level and above within 5km from the MDL".
The statement also said they had agreed to "participate jointly" at worldwide competitions including the 2020 Olympic Games in Tokyo.
The North Korean leader said he has agreed to visit Seoul in the near future.
"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.
Kim hailed his relationship with Moon, and said the pair would discuss "various issues.in a frank and open-minded manner".
Kim sent his sister Kim Yo Jong to Pyeongchang as his personal envoy, and the two leaders have since met three times as part of an ongoing diplomatic rapprochement.