The two leaders are meeting at Peace House, south of the demarcation line in the border truce village of Panmunjom.
Kim is the first North Korean leader to step foot in South Korea since the 1950-53 Korean War, and the two leaders are expected to discuss issues relating to peace and denuclearisation of the Korean peninsula.
The two leaders smiled and shook hands after which Kim gestured to Moon to cross over to North Korea briefly, which they did for a few steps, then returned to the South, holding hands.
The communist leader wrote in the guest visitor book at Peace House: “New history starts now; age of peace, from the starting point of history.”
North Korea and South Korea have never signed an official peace treaty after the Korean War.
The officials were escorted by South Korean honour guards to an official welcoming ceremony before beginning official dialogue at 10.30am.
The United States is hopeful that talks between North Korean leader Kim Jong Un and South Korean President Moon Jae-in will make progress on achieving peace and prosperity, the White House said in a statement on Thursday as the two men began their summit.
The White House also said it looks forward to continuing discussions with South Korea in preparation for the planned meeting of President Donald Trump and Kim in the coming weeks.
Three key issues will be on the agenda when the two leaders sit down together; improvement of inter-Korea relations after decades-long rivalry, a peace settlement, and denuclearisation of the Korean peninsula.
South Korea hopes Kim will directly confirm his will for “complete” denuclearisation of the peninsula.
The two countries are also expected to release a joint statement late on Friday, possibly called the Panmunjom Declaration, that could address issues surrounding the improvement of relations and peace.
KCNA news agency also stated Kim would plant a memorial tree with Moon at the meeting as a symbol of growing peace between the nations.
Just days before the summit, Kim said North Korea would suspend nuclear and long-range missile tests and dismantle its only known nuclear test site.
Moon travelled to the meeting in a large motorcade, stopping briefly to greet dozens of summit supporters waving South Korean flags near the Blue House.