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 at 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.