"They exchanged views and discussed ways to implement the Panmunjom Declaration and to ensure a successful US-North Korea summit," the Blue House said in a statement, adding Moon would make a personal statement on Sunday morning.
On Thursday Trump rattled the region by cancelling his meeting with Kim which had been due to take place in Singapore on June 12 citing "open hostility" from Pyongyang.
But within 24 hours he reversed course saying it could still go ahead after productive talks were held with North Korean officials.
The original decision to abandon the historic summit blindsided South Korea which had been brokering a remarkable detente between Washington and Pyongyang after months of Kim and Trump trading insults and threats of war.
Pictures released by the Blue House showed Moon also shaking hands with Kim's sister Kim Yo Jong, who has played a major public role in recent talks with the South, including leading a delegation across the border during February's Winter Olympics.
The spy chiefs from both sides were at the meeting according to the photos.
The meeting between Moon and Kim took place in a grand building on the North Korean side of Panmunjom, a surreal and heavily fortified village that lies between the two countries and marks the spot where the armistice ending the Korean War in 1953 was signed.
Only last month the two leaders met in the same village, with Kim famously inviting Moon to step briefly into the North before they both held talks in a building on the South's side.
Saturday's meeting is only the fourth time serving leaders of the two Koreas, who remain technically at war, have ever met.
Unlike last month's summit, which was held in front of live TV cameras, Saturday's meeting took place in utmost secrecy, with reporters only being told after the face to face had taken place.
The meeting is the latest remarkable chapter in a rollercoaster few months on the Korean peninsula. Last year Trump and Kim were threatening war after Pyongyang tested its most powerful nuclear bomb to date and launched test missiles it said were capable of reaching the United States.
Tensions were calmed after Moon grabbed an olive branch from Kim who offered to send a delegation to the Winter Olympics in South Korea, sparking a major detente that led to Trump agreeing to hold direct talks with Pyongyang.
But in recent weeks the summit had been thrown into doubt by increasingly bellicose rhetoric from both top US administration officials and Pyongyang.
Trump eventually pulled the plug on talks in a personal letter to Kim on Thursday.
But he left the door open to future meetings and Pyongyang's immediate reaction was to say it was willing to sit down "at any time", prompting Trump to reply that the Singapore summit could still take place.
Koh Yu-hwan, an expert on Korean relations at Dongguk University, said Saturday's meeting between Moon and Kim increased the likelihood of the Singapore summit taking place as originally intended.
"Today's summit is aimed at resolving the misunderstanding caused by communication glitches between Washington and Pyongyang and lay the groundwork for the US-North Korea summit," he told AFP.