Smiling and waving, South Korean President Moon Jae-in met Mr Kim at the border before talks begin.
At the summit venue, Mr Kim said that he hoped for frank discussions.
The historic meeting will focus on the North's recent indications it could be willing to give up its nuclear weapons.
In a moment rich with symbolism, Mr Kim and Mr Moon shook hands on both sides of the border in the demilitarised zone.
The South Korean president briefly stepped into the border into North Korea as well - an unexpected moment.
"I am happy to meet you," Mr Moon told Mr Kim, reports say.
The leaders were met by an honour guard in traditional costume on the South Korean side. The pair walked to the Peace House in Panmunjom, a military compound in the demilitarised zone (DMZ) between the two countries, to begin talks.
"A new history begins now - at the starting point of history and the era of peace," read the message Mr Kim wrote in a guestbook at the Peace House.
The White House said it was hopeful for talks would make progress toward peace and prosperity. The Korean summit is seen as a prelude to a proposed meeting between Mr Kim and US President Trump by early June, an unprecedented move as no sitting US president has met with North Korean leader.
At the summit, the two leaders will address North Korea's controversial nuclear weapons programme.
Seoul has warned that reaching an agreement to rid Pyongyang of its nuclear weapons will be "difficult". North Korea's nuclear and missile technology has advanced significantly since the sides' leaders last met more than a decade ago.
The meeting - the third of its kind following summits in 2000 and 2007 - is the result of months of improving relations between the two Koreas.
But Mr Kim's recent re-engagement and apparent concessions and have divided analysts, with some questioning the sincerity of his intentions.
Mr Kim announced last week that he would suspend nuclear tests for the time being.
The move was welcomed by the US and South Korea as a positive step, although Chinese researchers have indicated that North Korea's nuclear test site may be unusable after a rock collapse following its last test in September.
As well as addressing Pyongyang's nuclear ambitions, the leaders of the two Koreas are expected to discuss a path to peace on the peninsula to formally end the 1950-53 Korean War, and a series of economic and social issues.
Official talks between Mr Moon and Mr Kim began at 10:30 local time (01:30 GMT) at the Peace House in Panmunjom. The pair will break after the first session and will have lunch separately - with the delegation from the North crossing back to their side of the border.
At an afternoon ceremony, Mr Moon and Mr Kim will plant a pine tree using soil and water from both countries, to symbolise "peace and prosperity".