It is the first time in 65 years that the leaders from the North and South have come face-to-face, making it a rare moment in history and a potential turning point as the pair hold a summit with denuclearisation at the top of the agenda.
Mr Kim stepped over the border to greet his rival, and in an unchoreographed move, Mr Kim then invited Mr Moon to cross briefly North with him before they returned to the South for talks on Pyongyang’s nuclear weapons.
South Korea has said the Korean leaders have had “sincere and candid” talks on denuclearisation and are working on the wording of a joint statement.
“I feel like I’m firing a flare at the starting line in the moment of (the two Koreas) writing a new history in North-South relations, peace and prosperity,” Mr Kim told Mr Moon as they sat at a table.
Mr Moon responded that there were high expectations that they produce an agreement that will be a “big gift to the entire Korean nation and every peace loving person in the world”.
The two exchanged warm and encouraging words, with Mr Kim repeating “I am so glad to meet you”, and Mr Moon calling it “a pleasure”.
Mr Kim and Mr Moon poured a mixture of soil and water from both countries onto a pine tree they planted at a truce village as a symbol of peace before resuming their summit.
They also unveiled a stone plaque placed next to the tree that was engraved with a message saying Peace and Prosperity Are Planted.
The pine tree dates to 1953, the year the Korean War ended in an armistice.
The soil and water were brought from both the Koreas’ mountains and rivers.
The leaders then talked while walking unaccompanied on a nearby bridge before they are expected to resume the afternoon session of their summit at Panmunjom, a small village located in the the demilitarised zone separating the two Koreas.
Mr Kim at one point was seen waving away photographers as he and Mr Moon continued their talks sitting on chairs placed at the bridge.
The rival Koreas have a long history, having fought one of the 20th century’s bloodiest conflicts.
The divided peninsula is today still technically in a state of war.
It is still not clear whether the leaders can make any progress in closed-door talks on the nuclear issue – which has plagued US and South Korean officials for decades.
Expectations are low, given the collapse of previous breakthroughs.
The meeting comes ahead of a planned summit in several weeks between Mr Kim and Donald Trump.
Mr Kim will be keen to discuss the nearly 30,000 heavily armed US troops stationed in South Korea and the lack of a formal peace treaty ending the Korea War – the two factors Mr Kim cites as making nuclear weapons necessary.
Siobhan Robbins, Sky’s South East Asia Correspondent, said: “Both sides are acutely aware a breakdown of talks could catapult the peninsula towards fresh conflict or push the fiery and unpredictable Donald Trump to order a pre-emptive strike.
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“History has proven on this peninsula the road to peace is littered with failure.
“If, as many fear, in a few months the Kim family smiles turn out to be fake, the consequences for the world could be truly devastating.”