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 winner.
He will be formally sworn in at noon, forgoing the usual two-month transition because he was chosen in a special election after the last elected office-holder was removed by a court and jailed on corruption charges.
Taking up his role as the new commander in chief, Moon received a call from Army Gen. Lee Sun-jin, chairman of South Korea's Joint Chiefs of Staff, who briefed him on the military's preparedness against North Korea.
A short time later, Moon stepped out of his private home and received an emotional send-off from hundreds of residents, who shook his hand, hanged flowers on his neck and asked him to pose with his children. He then left with his wife, Kim Jeong-sook, for a national cemetery in Seoul.
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His Democratic Party has only 120 seats in the 300-seat National Assembly, so he may need broader support while pushing his key policies.
"I had a telephone call with Liberty Korea Party candidate Hong Joon-pyo. I again offer him words of comfort," Moon said during his visit to the conservative party, whose candidate Hong placed second.
Chinese leader Xi Jinping congratulated Moon on his election win, according to state media reports that provided no further details.
Relations with China have sunk to one of their lowest points since the two countries established diplomatic relations in 1992. Beijing objects to the US missile-defense system THAAD recently deployed in South Korea because it fears the system's radar could be used to monitor the Chinese military's flights and missile launches.
This softer approach might put him at odds with South Korea's biggest ally, the United States. The Trump administration has swung between threats and praise for North Korea's leader.
Moon was declared president after the election commission finished counting the votes, saying Moon gathered 41 percent, comfortably edging conservative Hong Joon-pyo and centrist Ahn Cheol-soo, who gathered 24 percent and 21 per cent, respectively.