"If needed I will fly to Washington immediately", said Moon - who backs engagement with North Korea.
He also needs to figure out how to ease tensions with China stemming from the deployment of a USA anti-missile defence system in South Korea that Beijing sees as a threat to its own security. A conservative challenger, former prosecutor Hong Joon-pyo, was next with 25.5 per cent followed by centrist candidate Ahn Cheol-soo with 21.4 per cent.
Mr Moon will be sworn in as South Korea's 19th president at a midday (03:00 GMT) ceremony at the National Assembly building.
South Koreans voted Tuesday in a presidential election a conservative candidate declared a "war of regime choices" in stark contrast to the liberal front-runner looking to overturn a decade of right-leaning rule.
Throughout his campaign, Moon has spoken figuratively of moving the base of power out of South Korea's version of the White House and into those squares where protesters gathered.
But analysts warn perceptions that the US ignored South Korean input on its own security issues - compounded when Trump called both Chinese President Xi Jinping and Japanese Prime Minister Shinzo Abe to discuss North Korea, but the caretaker government in Seoul - have left a key relationship strained before it has even begun. "And I will be the proud president of such a proud nation", Moon was quoted as telling his supporters earlier.
South Korea's presidential election has been won by Moon Jae-in, a liberal who favors a more open policy toward North Korea.
"We look forward to working with President-elect Moon to continue to strengthen the alliance between the United States and the Republic of Korea and to deepen the enduring friendship and partnership between our two countries", the statement said.
Domestically, Mr Moon begins his term facing multiple challenges, including the aftermath of the huge corruption scandal that saw his conservative predecessor Park Geun-hye impeached and swept him to power, but leaves the country bitterly divided.
Moon is inheriting a hard situation in light of the tense relationship between the United States and North Korea.
Marco Silva only focused on Hull's result against Sunderland
He added: "It's only important to win and to take the three points, and then we will see what the (Swansea) score is". He admits that the regret will remain that they could have produced such a performance earlier in the season.
"As we know, Korea has been hobbled by its political crisis that has stretched out over a number of months and quite legitimately, who would President Trump have talked to?" He will also name officials to the key positions of prime minister, head of the National Intelligence Service, chief of staff, and chief bodyguard, a parliament official said.
The imperial power of a president will be decentralized as much as possible, and agencies of power will be completely delinked from politics, Moon said, indicating a reform on the prosecution office. "It would take months for these tensions to sort themselves out, especially if Trump publicly criticizes the new South Korean president or penalizes Seoul, perhaps through trade measures", wrote Scott Seaman, director of Asia at think tank Eurasia Group, in a note to clients.
Tokyo, which has strained relations with its neighbour over issues including territory and Japan's wartime sex slavery, also congratulated Moon.
His election could add volatility to relations with Washington, given his questioning of the deployment of the US military's Terminal High Altitude Area Defences (THAT'D) anti-missile system, but is not expected to significantly change the alliance, a USA official said. The new South Korean president will still serve out a full, single five-year term.
Moon was a strong proponent of the "Sunshine Policy", an attempt to improve relations between the two Koreas from 1998 to 2008, and served as chief of staff to former South Korean President Roh Moo-hyun.
Taking office without the usual two-month transition, Moon initially will have to depend on Park's Cabinet ministers and aides, but he was expected to move quickly to replace them.
In just six months, Park went from the country's most powerful person to languishing in a jail cell as she awaits a corruption trial. Dozens of high-profile figures, including Park's longtime confidante, Choi Soon-sil, and Samsung's de facto leader, Lee Jae-yong, have been indicted along with Park.
Many analysts say Moon, if elected, likely won't pursue drastic rapprochement policies because North Korea's nuclear program has progressed significantly since he was in the Roh government a decade ago. Trump has voiced the possibility of unilateral action against North Korea, but also suggested that he would be honored to meet Kim Jong-un.
But the Trump administration has not been consistent, and, amid all the hostile posturing, the United States president has said he would be honored to meet with North Korea's leader.
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