The special election was necessitated by the ousting of conservative Park Geun-hye, whose downfall and jailing on corruption charges is one of the most turbulent stretches in the nation's recent political history.
He is facing a delicate task balancing ties with the US, Seoul's traditional ally, and China - both of whose help he needs to tackle North Korea and its nuclear ambitions.
On Thursday, North Korea expressed what it wants from the South's new government through the newspaper, instead of official bodies.
That's exactly what happened.
North Korea's state media Korean Central News Agency (KCNA) and other broadcasting channels released reports on Moon's election win on Thursday.
Many older people are wary of Moon's less confrontational stance on North Korea.
"Just spoke with my friend President Moon Jae-in".
Moon has said the decision had been made hastily and his government should have the final say on whether to deploy it.
Mr Moon has acknowledged that strong sanctions will be necessary to bring North Korea to the negotiating table.
"The global community has moved decisively toward a more sanctions and less engagement approach with North Korea and even South Korea's own domestic laws will make grandiose unaccountable inter-Korean engagement more hard", Marcus Noland and Kent Boydston of the Peterson Institute for worldwide Economics wrote in an analysis.
"What people who were protesting wanted was political change, and a natural effect of that is a change in government", Kang said.
"It's now time for the U.S.to review its policy of imposing pressure on North Korea over its nuclear program". Gee, this sounds familiar! "I will be a president who also serves all the people who did not support me". The exercises which mobilized US strategic assets ended in April. Technically, they remain at war. But Trump has also declared that he would be "honored" to meet with North Korean leader Kim Jong-un "under the right circumstances".
In the first direct contact between the South Korean and Chinese leaders, Xi explained China's position, Yoon Young-chan, a spokesman for South Korea's presidential office said without elaborating.
"It's going to take some budget, for items such as bulletproof glass", Song said, adding that Moon hoped to be in his new offices by 2019. He did not go into details, though. That is the approach Moon will need to persuade the Trump administration to adopt. "The alliance is more important than ever, given the rising uncertainty surrounding the Korean Peninsula". They agreed to closely cooperate in dealing with North Korea's nuclear weapons development program.
Despite Kim Jong-un showing his strength, Moon wants to soften the tone with the communist kingdom. China views THAAD as a threat to its own nuclear deterrent, because the Korea-based long-range radars had the capability to penetrate Chinese territory.
"If needed, I will fly to Washington immediately", Mr Moon said in his inauguration speech after taking the oath of office in front of lawmakers at Seoul's National Assembly building.
In his inaugural address Wednesday, South Korea's president said he would consider visiting Pyongyang under the right conditions. "Later, I will go back to my home and become an ordinary citizen", Moon said.
During his campaign, many conservatives anxious that Moon's election would cause problems with Washington, Seoul's most important ally, because of his engagement policy on North Korea would clash with Trump's push to maximize pressures on the country.
Moon said in a YouTube live stream on Tuesday South Korea should take on a more active diplomatic role to curb North Korea's nuclear threat and not watch idly as the United States and China talk to each other.