The president-elect said his victory came from the "desperation of the people for a new government".
Winning 41 percent of the votes, he comfortably edged conservative Hong Joon-pyo and centrist Ahn Cheol-soo, who had 24 percent and 21 percent, respectively.
South Korea's presidential candidate Moon Jae-in of the Democratic Party is greeted by supporters in front of his house in Seoul, South Korea, Tuesday, May 9, 2017.
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".
Born to a poor family that fled North Korea and settled in a small island in South Gyeongsang Province, Moon started his career as a radical pro-democracy activist and a human rights lawyer.
Moon, whose victory capped one of the most turbulent political stretches in the nation's recent history and set up its first liberal rule in a decade, assumed presidential duties after the National Election Commission officially declared him as victor.
Park is jailed awaiting trial later this month on bribery, extortion and other corruption charges.
The commission said turnout was high at 77.2 per cent of all eligible voters, up on the 2012 figure of 75.8 per cent, and much higher than the previous election, which only saw 63 per cent turn out to vote. Mr. Trump said South Korea should pay for operating the system, while Mr. McMaster later called his counterpart in South Korea to assure him that the USA would not insist on Seoul paying for it.
Liberal politician Moon Jae-in in Seoul.
Emmanuel Macron prepares groundwork for transition to power
European Parliament President Antonio Tajani told AFP: "We have received a vote of confidence from France in the European Union". Symbolically, Macron also said German Chancellor Angela Merkel will be the first foreign leader he will meet as president.
The win by Moon ends a decade of conservative rule in South Korea and could result in sharp departures from recent policy toward nuclear-armed North Korea.
Voting stations are set to close at 8 p.m. and South Korean TV stations plan to release the results of their joint exit polls soon after the vote ends and are expected to predict a victor before midnight. That is South Korea's formal name.
On the square, freelancer Koh Eun-Byul, 28, told AFP: "I am so happy because now there is hope for some meaningful change".
The son of refugees from North Korea, Moon was jailed while a student in the 1970s for leading protests against military ruler Park Chung-Hee - the father of impeached President Park Geun-Hye.
Moon is expected to be sworn in for a five-year term on Wednesday.
The 64-year-old Moon thanked people who stood with him to bring change.
"This is a great victory for the great people who have been with me to build a just country, united country and a country where principles and common sense work", Moon said at a rally in Seoul.
His election will likely be welcomed by Pyongyang, which on Monday called for "a new era of unification", urging the South to vote against conservatives, who were the "manic followers of confrontation". Park is now in jail awaiting trial on 18 charges, including bribery, over allegations that she took money from billionaire Samsung scion Lee Jae-yong in an effort by Lee to facilitate a major business transaction.
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