Moon and Kim were holding their summit at the headquarters of the Central Committee of the Workers' Party of Korea.
An airplane carrying Moon and his entourage, including presidential secretaries, cabinet members, businesspeople, lawmakers and entertainers, departed for the DPRK's capital city at around 8:50 a.m. local time (2350 GMT Monday).
Mr Moon and his wife, Kim Jung-sook, were greeted by Mr Kim and his wife, Ri Sol-ju.
Photo People watch the televised broadcast in Seoul of the Korean leaders meeting in Pyongyang.
They were greeted by thousands of cheering North Koreans waving flowers, North Korean flags and a blue-and-white map symbolising a unified peninsula.
They then inspected goose-stepping soldiers, and Moon shook hands with North Korean civilians and bowed deeply to them.
But U.S. officials remain "unenthusiastic" about declaring an end to the war without any substantial action toward denuclearization from the North, Seoul officials said.More news: Liverpool Boss Jurgen Klopp Delivers Staggering Virgin Analogy Ahead Of PSG Test
As a soldier, he served at the border village of Panmunjeom and was involved in an operation in the wake of the Axe Murder Incident in 1976, in which North Korean guards killed two USA officers who were cutting down a poplar tree in the Demilitarized Zone.
Moon's two late liberal predecessors, Kim Dae-jung and Roh Moo-hyun, went to Pyongyang in 2000 and 2007, respectively, to meet Kim's dictator father Kim Jong Il.
During their motor parade through Pyongyang's landmark Ryomyong Street, a new residential district launched past year under Kim's initiative to modernise the city, Kim and Moon briefly stepped out of the vehicle to greet and take flowers from members of the crowd.
"Thanks to that, the political situation in the region has stabilized and I expect more advanced results", Kim told Moon, according to South Korean press pool reports.
Moon will return home on Thursday.
Moon's office says the summit will focus on how to achieve denuclearization, reduce military tensions between the Koreas and promote ties. "I believe that the denuclearization issue can be progressed at a rapid pace if the two leaders face each other again and talk", said Moon.More news: 'Trying to attack me': Kavanaugh accuser reveals details of alleged sexual misconduct
Samsung's Lee Jae-yong and the heads of the SK and LG groups will be part of President Moon Jae-in's delegation as he heads for a meeting with the North's leader Kim Jong Un, Moon's office said.
This week's summit comes as the United States presses other countries to strictly observe U.N. sanctions aimed at choking off funding for Pyongyang's nuclear and ballistic missile programs.
Citing the lack of progress on U.S.
To keep expectations from getting too high, Moon's chief of staff, Im Jong-seok, said it's "difficult to have any optimistic outlook" for progress on denuclearization during the summit. Military officials have discussed possibly disarming a jointly controlled area at the Koreas' shared border village, removing front-line guard posts and halting hostile acts along their sea boundary. The navies of the Koreas have fought several bloody skirmishes off the west coast of the Korean Peninsula.
Luckily for the two leaders, it was a sunny and mild day in Pyongyang - but both of them could be seen trying to neaten their hair a bit as they arrived at the summit.More news: USA border agent charged in 2-week killing spree
"On the North's side, it would be a useful test of Pyongyang's sincerity to ask it to officially give up its claim to sovereignty over the South in the declaration", said Ralph Cossa, an Asia expert at the Pacific Forum.