According to South Korean officials, the meeting is set for April 27th at a border village.
The summit is expected to prove significant in the global diplomatic push to resolve the standoff over the North's nuclear programme.
"It is our hope that all people will become one so the summit can become a groundbreaking opportunity to establish peace on the Korean Peninsula", he added.
The previous editions of the summit were held in 2000 and 2007, both in the North Korean capital Pyongyang.
However, the North has yet to officially confirm its interest in a summit between the leaders.
Japan's government spokesman says his country has been in touch with North Korea, but refuses to say whether a possible meeting between their leaders is being discussed.
Chinese State Councilor Yang Jiechi is spending two days in Seoul briefing South Korean officials on the results of the talks between Kim and Xi.
Trump wrote on Twitter he had received a message from Xi late on Tuesday that his meeting with Kim "went very well" and that Kim looked forward to meeting the US president. Trump asked. "Because it's a very strong card and I want to make sure everyone is treated fairly, and everything is moving along very nicely with North Korea".
The talks followed a surprise meeting this week between Mr Kim and Chinese President Xi Jinping, which appeared to be aimed at improving both countries' positions ahead of the North Korean leader's planned meetings with Mr Moon and US President Donald Trump.
The trip was in part an effort to mend an old alliance which has been strained in recent years. The agenda will primarily focus on the denuclearization of the Korean peninsula, Reuters reported.
Kevin Rudd, former Australian Prime Minister and Asia Society Policy Institute President, told CNN there had been a wide misreading of Kim's statements on denuclearization.
The announcement comes after the North Korean leader reportedly said he was "committed to denuclearisation" during a visit to China.
"This language (of denuclearization) is not new, it's been around for quite a long time, and the core point is its highly conditional".
Trump and Kim had exchanged insults and veiled threats of war in recent months but the US leader made the surprising announcement this month that he was prepared to meet Kim to discuss the crisis over the North's development of weapons.
South Korean Unification Minister Cho Myong-gyon told reporters Kim's visit to China was not discussed with North Korean officials in their Thursday talks.
Seoul said the two sides reached an agreement on holding the summit at a meeting between special envoys of Kim and Moon in Pyongyang earlier this month.
The North Korean representative Ri agreed, saying visiting Tongil-gak was "emotional" for all Korean visitors.
"Just this week we secured a wonderful deal with South Korea, we were in a deal that was a horror show", Trump said.
Correction: The story has been updated to reflect that talks are being held on the northern side of Panmunjom.