The plane carrying Mr Moon left Seoul on Tuesday morning and flew in an indirect route off the west coast of the peninsula before turning inland and arriving at Pyongyang's Sunan International Airport about 80 minutes later, Mr Moon's office said.
This will be the fifth inter-Korean summit in the history of two Koreas and the third one this year.
Both Koreas likely have an ally in Beijing, which has always been wary of the U.S.
At his summit with Kim in June, Trump said the USA would halt "war games" with South Korea.
Both leaders want the U.S. to sign off on formally ending the Korean War, which still technically continues because no peace treaty has ever been signed.
The third summit comes as US-North Korea denuclearisation talks are in a stalemate.
-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.
US Ambassador to the United Nations Nikki Haley accused Russian Federation on Monday of "cheating" on U.N. sanctions on North Korea.
He said if that happens, coupled with a potential midterm election defeat for U.S. Republicans, "that would be disastrous".
There is a possibility of the president watching the "Brilliant Fatherland" mass gymnastics performance unveiled by the North on the occasion of its 70th founding anniversary earlier this month following the summit talks or art performance.
"I wish this will be a summit that produces abundant results as a gift to the 80 million people of this nation for Chuseok", the South Korean leader said, referring to the traditional holiday that falls on Monday.
The summit came a day after U.S. U.N. Ambassador Nikki Haley called out Russian Federation and China for consistently skirting U.N. sanctions against North Korea, during an urgent Security Council meeting called by the U.S. The sanctions are aimed at pressuring the regime to abandon its nuclear and missile programs.
"Citing the lack of progress on U.S. - North Korean dialog, Kim said, "[South Korea] needs to have some kind of mediating role to (continue dialog)". At the time, the North Korean leader declared his backing for the denuclearisation of the peninsula.
Every year on September 9, North Korea celebrates its birthday by holding a military parade in the capital, Pyongyang. "North Korea [second] summit meeting, [and] no peace declaration".
"Unsurprisingly, therefore, we insisted on having our position reflected in the document", he said, and a compromise on the report was reached among all 15 council members - including the "American delegation" and USA "experts".
South Koreans appetite for unification has fallen as the differences between the two countries grow and the expected costs of reunification rise.
Currently, all major joint projects between the Koreas are stalled because of US-led sanctions.
Saying that he seeks a peace unaffected by worldwide politics, Moon went on to say that building a permanent peace is the path to unification, adding he will focus on two elements.
They are: Lee Hae-chan, leader of the ruling Democratic Party; Chung Dong-young, leader of the minor opposition Party for Democracy and Peace; Lee Jeong-mi, leader of the liberal-leaning Justice Party and Rep. Park Jie-won of the Party for Democracy and Peace.
An undated photo shows a march for peace, prosperity and reunification of Korea in Pyongyang, North Korea. That's important because China is the North's biggest economic partner and is an important political counterbalance to the United States.
"It is due to its nonsensical, irrational stubbornness that other issues can only be discussed after our country has completely verifiably, irreversibly dismantled our nuclear capabilities ... without showing the intention to build trust including declaring the end of war", the newspaper said in an editorial.