The US President and North Korean leader are due to meet in Hanoi from February 27 to 28 following their landmark first summit in Singapore last June.
That meeting -- the first-ever between the leaders of the US and North Korea -- produced a vaguely-worded document in which Kim pledged to work towards "the denuclearisation of the Korean peninsula".
But progress has since stalled with the two sides disagreeing over it means and analysts say tangible progress on denuclearisation will be needed if the talks are to avoid being dismissed as "reality TV".
With the high-stakes summit now two weeks away, Pyongyang has yet to provide any official confirmation of the meeting in the Vietnamese capital.
"For us, the era of peace and prosperity on the peninsula has drawn closer," said Moon in his first comments since the summit was announced.
The meeting was a "remarkable breakthrough in the peace process on the Korean peninsula", the South Korean president added.
But he acknowledged there were "still many doubts about whether the denuclearisation of the Korean peninsula and peace process can be concluded successfully".
The leaders of the two Koreas and the US have persisted in talks over the issue because of "strong confidence in the direction history should take", added Moon, who has taken on the role of middle man between Pyongyang and Washington, trying to bridge the gap on denuclearisation talks.
Security allies Seoul and Washington have at times pursued divergent approaches toward Pyongyang, with the dovish South Korean leader pursuing engagement while the United States insists pressure must be maintained until the North denuclearises.
But Moon expressed gratitude to both Trump and Kim for their "unprecedented, bold diplomatic efforts", saying they were "crossing a sea of deep mistrust".