In the first summit between the two countries since 2007, Kim crossed the military demarcation line at 9:30am (0:30 GMT) on Friday for a meeting in Panmunjom’s Peace House.
It is only the third time leaders of the two Koreas have met since an armistice agreement ended the Korean War in 1953, and the first time a summit has taken place in the South.
The truce is still in force and Kim and Moon were expected to discuss a more permanent solution on Friday.
North Korea halted its nuclear and missile test programme last Saturday, raising hopes that the country was serious about negotiating full denuclearisation.
But on Wednesday, questions were raised about the motives behind the pause, when it was reported that North Korea’s test site had allegedly collapsed and was “wrecked” beyond repair.
Reporting from Paju, South Korea, Al Jazeera’s Diplomatic Editor James Bays said the US would monitor the inter-Korean meeting closely, with a later meeting planned between President Donald Trump and Kim still hanging in the balance.
“The Trump administration in Washington will be looking that there’s no hiccups in this, that it runs extremely smoothly and that I think will then give them the confidence to go ahead with this other even more important summit,” he said.
Trump has said he plans to meet Kim by early June.
Kim’s sister, Kim Yo-Jong, who visited South Korea during the Pyeonchang Winter Olympics in February, was expected to be part of the North’s delegation of nine, excluding Kim himself.
He was also to be joined by Kim Yong-chol, a former spymaster, and Kim Yong-nam, the president of the country’s legislative body and ceremonial head of state.
Among South Korea’s delegation of seven are the country’s minsters for defence, foreign affairs and unification.
Kim and Moon are expected to sign a pact and make a joint statement at the end of the talks.
The day’s events will be full of symbolism.
In the afternoon, Kim and Moon will plant a tree on the demarcation line using soil from both the north and the south, which they will water with water from the North’s Taedong River and the South’s Han River.
For dinner, the leaders will be served plates with the Swiss potato dish rosti, a nod to Kim’s childhood allegedly spent at a boarding school in the Alpine country, and baked John Dory – a fish which is popular in Moon’s hometown of Busan.