Left-leaning Moon Jae-in is the clear front-runner with centrist Ahn Cheol-soo his nearest challenger.
The election is being closely watched at a time of economic uncertainty and heightened tensions with North Korea.
Mr Moon wants to increase contact with the North in contrast to ex-leader Park Geun-hye who cut almost all ties.
Observers are expecting a high turnout at the ballot boxes, with numbers boosted by younger voters, as South Koreans choose from 13 candidates.
Polls close at 20:00 local time (11:00 GMT), with the winner expected to be announced soon after.
Money and jobs
All the candidates are promising to protect the fragile recovery in South Korea's economy - the fourth largest in Asia - and to bring down youth unemployment, which remains stubbornly high.
There are also promises to rein in perceptions of elitism in South Korean political society and reform the family-run conglomerates - chaebols - which dominate the domestic economy.
Economic issues are among voters' top concerns
Keeping an eye on the North
But heightened tensions on the Korean peninsula in recent weeks has also made the perennial concern of domestic security a key election concern.
Mr Moon, of the Democratic Party of Korea, has advocated greater dialogue with the North while maintaining pressure and sanctions.
He has been critical of the two previous conservative administrations for failing to stop North Korea's weapons development.
Conservative candidate Hong Joon-pyo of the Liberty Korea Party however has attacked Mr Moon's approach, saying on Thursday morning that the election was a "war of regime choices".
Mr Moon (left) cast his vote with his wife Kim Jeong-suk (right) on Tuesday morning
New blood at the top
Candidates are also promising a break from the past as symbolised by the deeply unpopular Ms Park.
Mr Moon, has called for an "overwhelming victory" as it would help to heal a national divide caused by her impeachment.
"I feel that not only my party and myself but also the people have been more desperate for a change of government," he told reporters on Tuesday morning after he cast his vote.
Ahn Cheol-Soo is a former medical doctor turned software tycoon
In March, Park Geun-hye became the first South Korean president to be removed from power by impeachment.
She denies wrongdoing - although she has repeatedly apologised - and is standing trial on charges of bribery and abuse of power.
Mr Moon narrowly lost to Ms Park in the last presidential election in 2012.
Mr Ahn had also run for the job but dropped out to endorse Mr Moon in an attempt to consolidate votes against Ms Park. He has now positioned himself as an alternative to Mr Moon, promising to be tougher on national security.
"The time for Ahn Cheol-soo is here and the time for Moon Jae-in is slipping away," he declared in his campaign.