He vowed to address the economy and relations with North Korea in his first speech as president.
Moon Jae-in, 64, said that he would even be willing to visit Pyongyang under the right circumstances.
He took his oath of office in Seoul’s National Assembly building a day after his victory.
The former human rights lawyer and son of North Korean refugees is known for his liberal views.
Tensions on the Korean peninsula remain high and recent weeks have seen the US and North Korea trade angry rhetoric as speculation about another nuclear test grows.
Moon Jae-in has also vowed to unify a divided country reeling from a corruption scandal which saw his predecessor, Park Geun-hye, impeached.
In his inauguration speech, Moon Jae-in said he would “do everything I can to build peace on the Korean peninsula”.
“If needed I will fly to Washington immediately,” he said.
“I will also go to Beijing and Tokyo and even Pyongyang in the right circumstances.”
Moon Jae-in added that he would have “serious negotiations” with the US and China over the controversial deployment of anti-missile system THAAD.
North Korea has yet to officially comment on Moon Jae-in’s victory and remarks. It had previously hinted that Moon Jae-in was its preferred candidate.
The Democratic Party candidate has also promised to bolster the economy and address youth unemployment, which are key concerns for voters.
Moon Jae-in has been critical of the two previous conservative administrations, which took a hard-line stance against Pyongyang, for failing to stop North Korea’s weapons development.
Since the Korean War ended in an armistice in 1953, there have only been two summits where the leaders of the two Koreas have met, both held in Pyongyang.
Moon Jae-in spearheaded preparations for the second meeting in 2007, when serving as a presidential aide.
The US, South Korea’s most important ally, has congratulated Moon Jae-in on his victory.
White House press secretary Sean Spicer said the US looked forward to continuing to “strengthen the alliance” and “deepen the enduring friendship and partnership”.
Japan’s PM Shinzo Abe said their countries faced common challenges “led by responses to the North Korean issue” but they could “further contribute to peace and prosperity of the region by working together”.
China’s President Xi Jinping said he “always attaches great importance to the relationship between China and South Korea”, and that he was “willing to diligently work with” with Moon Jae-in to ensure both countries benefit, reported Chinese state news agency Xinhua.
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