Mr Kim and his wife, Ri Sol-ju, walked out on to the tarmac when President Moon's plane landed at Pyongyang's global airport.
Since taking office in May previous year, Mr Moon has met Mr Kim twice at the Koreas' shared border village of Panmunjom.
It was also a first when Moon and Kim walked along the red carpet at Pyongyang's Sunan International Airport and the South Korean leader inspected North Korean troops.
"You Mr. President are travelling all around the world, but our country is humble compared with developed nations", Kim told Moon.
The nuclear-armed North invaded its neighbor in 1950, starting the Korean War, and regularly stresses the importance of reunifying with the now far wealthier South. As a military band played a rousing march, thousands of North Koreans, lined up in neat rows and dressed in black suits and traditional hanboks, cheered and waved bouquets of artificial flowers, the North Korean flag and a white-and-blue flag with a map symbolizing a unified Korean Peninsula. "-North Korean dialog, Kim said, "[South Korea] needs to have some kind of mediating role to [continue dialog]".
Kim and Moon embraced at Pyongyang's global airport - where the North Korean leader had supervised missile launches past year as tensions mounted.
According a joint statement signed by the countries' defence chiefs, the two Koreas agreed to establish buffer zones along their land and sea borders to reduce military tensions and prevent accidental clashes.
"This is not a matter on which we can take the lead, so (I) hope to speak frankly with Chairman Kim Jong-un to find a middle ground between the US' demands for denuclearization and the North's demands for ending hostilities and ensuring safety (of the regime)".
"Second is facilitating North-US talks for denuclearization".
"(My) North Korea trip would have a great meaning if it could lead to the resumption of North Korea-U.S. dialog", Moon was quoted as telling his aides before departing from Seoul. -North Korean relations back on track, Moon might try to, among other things, seek more reassurance from North Korea that an end-of-war declaration would not mean the withdrawal of US troops from South Korea, Aum said.
Officials say many of Moon's official events in Pyongyang, including the leaders' opening summit remarks, will be broadcast live in South Korea.
The Latest: South Korea president leaves for North Korea
Kim and Moon got into separate vehicles at Pyongyang airport before driving away.
But when North Korea did not show enough effort to denuclearize after the first 2018 Inter-Korean Summit, President Trump threatened that the meeting between him and Kim Jong-un might not take place.
Talks between the United States and North Korea, which Moon brokered through his April and May summits with Kim, have stalled since Kim's meeting with President Donald Trump in Singapore in June.
The primary focus of Moon's trip is to address ways to reduce tension on the Korean Peninsula and avoid armed conflict between the two countries.
"I hope this summit can produce a fruitful result as a gift for the Chuseok holidays for 80 million people", he continued - a reference to the upcoming Korean holiday.
FILE - In this May 24, 2018 file photo, command post facilities of North Korea's nuclear test site are exploded in Punggye-ri, North Korea.
After the first-day talks, a welcoming art performance and welcome dinner will be held.
On Wednesday, Moon and Kim plan to hold a second round of talks after which they are expected to unveil a joint statement and a separate military pact created to defuse tensions and prevent armed clashes. Currently, all major joint projects between the Koreas are stalled because of USA -led sanctions.
Moon and Kim are expected to give a joint press conference on Wednesday.
With North Korea hard-pressed by worldwide sanctions, it is unlikely that the third inter-Korean summit will yield immediate results in such areas as cross-border economic cooperation.