The election follows months of political turmoil stemming from a parliamentary vote in December to impeach former president Park Geun-hye over an extensive corruption scandal.
Moon was chief of staff for the last liberal president, the late Roh Moo-hyun, who sought closer ties with North Korea by setting up large-scale aid shipments to the North and by working on now-stalled joint economic projects.
"I will make a just, united country", Moon told a crowd gathered just before midnight to see the former human rights lawyer who entered politics to lead a party just five years ago.
Liberal candidate Moon Jae-In won South Korea's special election over the conservative challenger with a plurality of the vote, receiving 41.4% of the ballots in his favor.
Yonhap reported Ahn conceded defeat before the official announcement, and the Liberty Party Korea's Hong told reporters earlier in the evening that he would be "satisfied with restoring his party", referring to the deep divisions that beset Korea's conservatives after the impeachment of Park for her involvement in a corruption scandal that enriched her friend Choi Soon-sil.
Moon Jae-in, the presidential candidate of the Democratic Party of Korea, poses for photographs as he watches a television report on an exit poll of the presidential election in Seoul on Tuesday. "But if things go on this way and we win, today's victory is thanks to sheer desperation of the people who wanted a regime change".
But whoever becomes president could also dramatically alter the current state of affairs on the Korean Peninsula starting day one - the victor will immediately take charge.
Such animation is a big part of election day TV in South Korea.
Public sentiment in South Korea has already begun to sour towards Washington after President Trump said last month that Seoul should be paying for the Terminal High Altitude Area Defense (THAAD) system, contradicting the original mutual agreement in which Seoul would provide land and infrastructure.
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Voters were mainly focused on corruption and the economy, but North Korea loomed large over the election after weeks of rising tensions between Pyongyang and the USA administration under President Donald Trump.
Before the election, the North Korea government asked South Koreans to vote for a more liberal candidate.
Despite unusually high level of undecided voters due to split in the conservative camp and tight election schedule, turnout was exceptionally high at 77.2 percent. He has said he would be "honored" to meet Kim Jong Un, if the conditions existed for such a summit.
The election is being closely watched overseas at a time of high tension with North Korea, which is believed to be preparing for a sixth nuclear test and has vowed to test an intercontinental missile.
Only between 22 percent and 25 percent of people in their 60s and 70s voted for Moon, exit polls showed, underscoring a long-standing generation gap.
Meanwhile, Trump has called forexerting "maximum pressure" on North Korea to give up its nuclear and missile programs-programs that appear to have accelerated in recent months.
One issue on which they do differ remains the controversial Terminal High Altitude Area Defense (THAAD) missile defense system, deployed by the USA on South Korean soil and switched on last week.
The scandal surrounding former president Ms Park highlighted widening inequality and the corrupt ties between regulators and powerful companies, a relationship numerous candidates have vowed to reform.
During the Sunshine Policy, Seoul actively engaged Pyongyang, which led to closer relations on both sides of the border and saw two South Korean Presidents visit the North Korean capital.
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