Liberal Moon Jae-in has declared victory in South Korea's presidential election after his two major rivals conceded defeat.

The election sets up the country's first liberal rule in a decade.

A decisive win by Moon in a field of 13 candidates, puts an end to months of political turmoil stemming from a parliamentary vote in December to impeach former President Park Geun-hye over an extensive corruption scandal.

The concessions by conservative Hong Joon-pyo and centrist Ahn Cheol-soo came after exit polls forecast that Mr Moon would win.

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Liberal Moon Jae-in celebrates with supportesr after declaring victory in South Korea's presidential election after his two major rivals conceded defeat

South Chungcheong governor An Hee-jung kisses South Korea's president-elect Moon Jae-in at Gwanghwamun Square in Seoul

South Korea's president-elect Moon Jae-in thanks supporters at Gwanghwamun Square in Seoul following the election

Moon pledged Tuesday to represent all the country's people.

'I will be president for all South Koreans,' he told cheering supporters on Gwanghwamun Square in Seoul.

Exit polls projected Moon would take 41.4 per cent of the vote, 18 percentage points ahead of his nearest challenger.

'This is a great victory of great people who stayed with me to create a country of justice... where rules and common sense prevail,' he said.

South Korea was plunged into political turmoil by the scandal surrounding Park - who is now in custody awaiting trial - and Moon promised to be a 'president of cohesion' who also took care of those who did not support him.

The Constitutional Court upheld Park's impeachment in March, making her the first democratically elected leader to be removed from office and triggering a snap election to choose her successor.

South Korean presidential candidate Moon Jae-in of the Democratic Party of Korea reacts after a television report on an exit poll of the new president at the party's auditorium in the National assembly on Tuesday

Wearing a dark blue suit and blue tie, Moon was seen shaking hands with supporters and party officials and smiling on his way to a meeting of his Democratic Party after the exit poll results were announced

Supporters of the presidential candidate Moon Jae-in of the Democratic Party react as they watch televisions broadcasting results of exit polls for presidential election at National Assembly in Seoul

Supporters of presidential candidate Moon Jae-in react as they watch results of the presidential election in Seoul

Wearing a dark blue suit and blue tie, Moon was seen shaking hands with supporters and party officials and smiling on his way to a meeting of his Democratic Party after the exit poll results were announced.

A Gallup Korea poll last week showed Moon had 38 percent support in a field of 13 candidates.

Moon is expected to be sworn in on Wednesday after the National Election Commision releases the official result. He has said he would skip a lavish inauguration ceremony and start work straight away.

He is likely to quickly name a prime minister, who will need parliamentary approval, and main cabinet positions, including national security and finance ministers, which do not need parliamentary confirmation.

Moon, who narrowly lost to Park in the last presidential election, in 2012, favours dialogue with North Korea to ease rising tension over its accelerating nuclear and missile programme.

He also wants to reform powerful family-run conglomerates, such as Samsung and Hyundai, and boost fiscal spending to create jobs.

Moon has criticised the two former conservative governments for failing to stop North Korea's weapons development.

Moon, front left, of the Democratic Party takes pictures with a supporter after voting for a presidential election at a junior high school in Seoul, South Korea on Tuesday

South Korean presidential candidate Moon Jae-in of the Democratic Party and his wife Kim Jung-suk wave after voting on Tuesday. South Koreans voted Tuesday for a new president, with victory widely predicted for a liberal candidate who has pledged to improve ties with North Korea, re-examine a contentious U.S. missile defense shield and push sweeping economic changes

Outspoken conservative Hong Joon-pyo, the candidate from Park's Liberty Korea Party, described the election as a war between ideologies and questioned Moon's patriotism.

He advocates a two-track policy of dialogue while maintaining pressure and sanctions to encourage change.

Moon faces working with a fractured parliament where his Democratic Party holds 40 per cent of the single-chamber, 299-seat assembly, which will likely mean difficulties and deals to pass bills.

'He has to pursue cooperation with other liberal and centrist parties, since the Democratic Party does not have the majority,' said Kim Man-heum, head of the Korea Academy of Politics and Leadership.

'Moon has been criticized for running his own 'clique', so in order to get over that negative image, he'll seek cooperation to avoid rifts and conflicts,' Kim said.

His victory was bolstered by strong support from younger people, the majority of whom voted for him, according to the exit polls. Many of his supporters participated in big, peaceful weekend rallies over the last few months of 2016 and early this year, demanding Park step down.

The vote was the culmination of a frenzied two-month race set up by the scandal that ousted Park-Geun-hye, now jailed while awaiting trial on corruption charges.

Conservatives worry that a victory by the liberal, Moon Jae-in, might benefit North Korea and estrange South Korea and its most important ally, the United States.

Outspoken Hoon described the election as a war between ideologies and questioned Moon's patriotism.

Moon Jae-in of the Democratic Party and his wife Kim Jung-suk prepare to cast their ballot for a presidential election

Hong Joon-Pyo (L) of the Liberty Korea Party and his wife Lee Soon-Sam (R) cast their votes in the presidential election at a polling station in Seoul

South Korea's presidential candidate Ahn Cheol-soo of the People's Party comes out of a polling booth to cast his ballot for presidential election at a local polling station in Seoul

The vote was the culmination of a frenzied two-month race set up by the scandal that ousted Park-Geun-hye (pictured), now jailed while awaiting trial on corruption charges.

After voting, Hong said the election was a 'war of regime choices between people, whether they decide to accept a North Korea-sympathizing leftist government or a government that can protect the liberty of the Republic of Korea', South Korea's formal name.

Hong has pitched himself as a 'strongman' who can hold his own against other 'nationalist' leaders in Washington, Tokyo and Beijing.

He had called for the United States to bring back tactical nuclear weapons to South Korea after withdrawing them in the 1990s.

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.

Voting stations closed at 8pm and South Korean TV stations released the results of their joint exit polls soon after the vote ends.

The National Election Commission said more than 55 per cent of the country's 42.4million eligible voters cast their ballots as of 1pm, a measurement that included the 11million people who participated in early voting last week.

The winner will be sworn in after the National Election Commission confirms the result Wednesday.

Women walk by posters showing candidates for the presidential election in Seoul, South Korea on Tuesday

People gather to watch live broadcasts of coverage of South Korea's presidential election, in Gwanghwamun square in Seoul

South Koreans went to the polls to choose a new president after Park Geun-Hye was ousted and indicted for corruption, against a backdrop of high tensions with the nuclear-armed North. Pictured above, people gather to watch live broadcasts of coverage of South Korea's presidential election, in Gwanghwamun square in Seoul

Because the vote is a special election, the new president will forgo the usual two-month transition and will serve one full, five-year term rather than only completing Park's original term, which was to end in February 2018

Because the vote is a special election, the new president will forgo the usual two-month transition and will serve one full, five-year term rather than only completing Park's original term, which was to end in February 2018.

Park's trial later this month on bribery, extortion and other corruption charges, could send her to jail for life if she is convicted.

The allegations incensed many in South Korea, with millions taking to the streets in protest.

Park sympathizers later staged their own rallies. 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.

Moon frequently appeared at anti-Park rallies and the corruption scandal boosted his push to re-establish liberal rule.

He called for reforms to clean up social inequalities, excessive presidential power and corrupt ties between politicians and business leaders.

Many of those legacies dated to the dictatorship of Park's father, Park Chung-hee, whose 18-year rule was marked by both rapid economic rise and severe civil rights abuse.

As a former pro-democracy student activist, Moon was jailed for months in the 1970s while protesting against the senior Park.

Moon has called Park Geun-hye's hard-line North Korea policy a failure.

Voting stations are set to close at 8pm and South Korean TV stations plan to release the results of their joint exit polls soon after the vote ends. They are expected to predict a winner before midnight

The winner will be sworn in after the National Election Commission confirms the result Wednesday

Voters form a queue to cast their ballots at a polling station in Incheon, South Korea, on Tuesday

A woman casts her ballot for presidential election at a local polling station in Seoul, South Korea on Tuesday

Moon said as president he plans to employ both pressure and dialogue to persuade the North to abandon its nuclear ambitions. He also advocates building up a more assertive South Korea.

Following a standoff between President Donald Trump and North Korean dictator Kim Jong Un over Kim's vow to advance his country's nuclear weapons programs, Moon has talked more about bolstering national defense in what analysts see as an attempt to woo conservative voters.

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.

A big challenge for whoever wins will be President Donald Trump, who has proven himself unconventional in his approach to North Korea, swinging between intense pressure and threats and offers to talk.

'South Koreans are more concerned that Trump, rather than North Korean leader Kim Jong Un, will make a rash military move, because of his outrageous tweets, threats of force and unpredictability,' Duyeon Kim, a visiting fellow at the Korean Peninsula Future Forum in Seoul, wrote recently in Foreign Affairs magazine.

'It is crucial that Trump and the next South Korean president strike up instant, positive chemistry in their first meeting to help work through any bilateral differences and together deal with the North Korean challenge.'