The ballot was needed after Park Geun-Hye was ousted and indicted for corruption, and took place against a backdrop of high tensions with the nuclear-armed North.
Voters were galvanised by anger over the sprawling bribery and abuse-of-power controversy that brought down Park, which catalysed frustrations over jobs and slowing growth.
They gave Moon, of the Democratic Party, who backs engagement with the North, 40.2 percent support -- some 11.4 million votes -- according to the National Election Commission (NEC).
Conservative Hong Joon-Pyo -- who dubs Moon a "pro-Pyongyang leftist" was far behind on 25.2 percent, with centrist Ahn Cheol-Soo third on 21.5 percent.
Fewer than 4.2 million votes cast in the election were still to be counted and the NEC was expected to name Moon the president-elect after its official vote count was completed.
The result was "a great victory of great people" who wanted to create "a country of justice... where rules and common sense prevail", Moon told cheering supporters on Gwanghwamun Square in Seoul -- where vast crowds gathered for candlelit protests over several months to demand Park's removal.
The graft scandal plunged the country into political turmoil and bitter division, but Moon promised healing, telling the crowd: "I will be president for all South Koreans."
On the square among the crowd, Koh Eun-Byul, 28, told AFP: "I am so happy because now there is hope for some meaningful change."
Washington, which remains Seoul's most important ally and has a large security presence in the South, on Tuesday congratulated Moon on his landslide victory.
"We look forward to working with president-elect Moon to continue to strengthen the alliance between the United States and the Republic of Korea and to deepen the enduring friendship and partnership between our two countries," White House press secretary Sean Spicer said in a statement.
National elections are public holidays in South Korea and figures showed a turnout of 77.2 percent -- the highest for 20 years in a presidential poll.
