The meeting with Moon Jae-in is only the third time that leaders of the two countries have met in the 65 years since the Korean War – and the first time one of the Kim leaders has crossed over to the South.
The two leader shook hands on the border line before Mr Kim crossed into the South. Mr Moon later crossed into the North as well, and the two posed for ceremonial photos facing each side. The event was also attended by school children, an honour guard and a military band. It was broadcast live across South Korea.
The ceremony took place outside the Peace House, a conference building on the south side of the border, where the two leaders planned to discuss the issue of nuclear weapons on Friday.
North Korea's nuclear arsenal has developed rapidly in the last year, leading to tense exchanges between Mr Kim and US President Donald Trump. But the North and South have also made several unexpected steps toward peace, including marching under the same flag in the 2018 Pyeongchang Olympics.
The Olympics plan was hatched during an earlier meeting between North and South Korean diplomats, which went smoothly but skirted around the issue of nuclear weapons. This time around, North Korea's state news agency said Mr Kim would "open-heartedly" discuss "all the issues arising in improving inter-Korean relations and achieving peace, prosperity and reunification of the Korean peninsula" with Mr Moon.
Mr Kim has also made plans to meet with Mr Trump, in what would be the first in-person meeting between a US and North Korean president in history. The North Korean leader has already met with Mike Pompeo, the director of the CIA, in preparation for the summit.
The White House issued a statement on the inter-Korean summit on Thursday, saying the US was "hopeful" about the talks, and looked forward to the meeting between Mr Kim and Mr Trump.
Both the US and South Korea would like to see the denuclearisation of the North, which is close to building a nuclear missile capable that can reach the US. Mr Kim has said he is open to discussing the denuclearisation of the Korean Peninsula with both leaders, but experts say he will likely require tough concessions from the Americans.
Among other things, Mr Kim has taken issue with the US soldiers stationed in South Korea, the joint military exercises the two countries perform, and the lack of a formal peace treaty to end the Korea War. He also wants the US to remove its nuclear umbrella over the Penninsula and the Northeast Asian region.
South Korea and the US have slightly different ideas about how to denuclearise the North, with Mr Moon favouring a step-by-step process and Mr Trump calling for the immediate destruction of the country's nuclear weapons.
Mr Moon is likely setting the stage to serve as a mediator between the US and the North in this week's meeting, having acknowledged that any long-term solution on the Peninsula will require American input.
“Peace on the Korean Peninsula cannot be achieved by agreements between South and North Korea alone,” he said last month. “It has to have American endorsement.”