The announcement came a day after the North boasted a "successful" launch of the longest-range missile.
The summit will be held in Washington in late June, Yoon Young-Chan said, adding that details of the precise date and agenda would be decided later.
Moon backs engagement with nuclear-armed North Korea to try to reduce tensions, while Trump's administration has said military action was an option under consideration.
"We will prepare the summit as an opportunity to cement personal ties and friendship between the two leaders," Yoon said.
The announcement came a day after the North boasted a "successful" launch of the longest-range missile it has ever tested, sparking global alarm.
Tensions have been ratcheted up as Pyongyang and Washington exchanged hostile rhetoric, but Trump recently softened his posture, saying he would be "honoured" to meet the North's leader Kim Jong-Un.
Sunday's missile launch angered the White House which said the North had "been a flagrant menace for far too long" and called for tougher sanctions against Pyongyang.
Moon has said he would be willing to visit the North "in the right circumstances", but also slammed Sunday's launch as a "reckless provocation", saying dialogue would be possible "only if the North changes its attitude."
Tuesday's announcement came as Matt Pottinger, senior director for Asian affairs at the US National Security Council, vowed joint efforts to curb the North's military ambitions during a visit to Seoul.
Pottinger and his South Korean counterpart agreed that the two allies would seek "bold and practical" approach over the North, with dialogue with Pyongyang possible but only "when conditions are right", Yoon said.