This would be the third meeting this year between the two leaders, who will discuss "practical measures to denuclearise" the flashpoint peninsula during the September 18-20 summit, South Korean National Security Advisor Chung Eui-yong told reporters.
The summit dates were finalised during Chung's Wednesday visit to Pyongyang, where he met Kim and handed over a personal letter from Moon.
The North Korean leader said he is willing to cooperate with both Seoul and Washington on denuclearisation, according to the envoy.
During the meeting, the North Korean leader "expressed a firm determination toward complete denuclearisation of the Korean peninsula as well as an intention to work closely with the US... to achieve the goal", Chung said.
The South Korean envoy's visit to Pyongyang came amid a deadlock on the North's atomic weapons, with US efforts to dismantle the arsenal stalled for weeks.
In a landmark summit in Singapore in June, US President Donald Trump and Kim vowed to work toward the "complete denuclearisation of the Korean peninsula", but their agreement was short on details on what that meant and how it would be achieved.
Frustrated with the lack of progress, Trump last month cancelled Secretary of State Mike Pompeo's trip to Pyongyang after the North reportedly sent a belligerent letter to the US leader.
But despite the difficulties, Kim's "trust in Trump remains unchanged", Chung said.