The son of refugees from North Korea, Mr Moon was jailed while a student in the 1970s for leading protests against military ruler Park Chung-hee - Ms Park's father.
Later, he served in South Korea's special forces before becoming a human rights lawyer.
He served as a senior aide to liberal President Roh Moo-hyun, who killed himself in 2009 after leaving office amid bribery allegations.
Mr Moon, of the centre-left Democratic Party, unsuccessfully ran against Ms Park in the 2012 elections.
He has positioned himself as the man who can move the country on from the scandals of Ms Park's era.
"I feel that not only my party and myself but also the people have been more desperate for a change of government," he said while casting his vote.
What are his policies?
Mr Moon has advocated greater dialogue with the North while maintaining pressure and sanctions, in contrast to Ms Park who cut almost all ties.
He has been critical of the two previous conservative administrations for failing to stop North Korea's weapons development.
But while tensions on the Korean peninsula ensured the election was closely watched internationally, for South Koreans the priority has been corruption and the economy, with youth unemployment stubbornly high.
Mr Moon has talked of reforming South Korea's huge family-run conglomerates, known as chaebols, which dominate the domestic economy.