Security is tight, and four minor blasts were reported in the northern Tamil city of Jaffna.
President Mahinda Rajapaksa is facing a tough test against his former army chief General Sarath Fonseka.
Former allies, they became bitter rivals when Gen Fonseka decided to run for the presidency.
More than 14m voters are eligible to vote in 11,000 centres. Polls will close at 1600 local time (1030 GMT).
Counting will begin three hours later and the final results are expected to be announced on Wednesday morning, the election commission has said.
There are 22 candidates standing for the presidency.
If no candidate has 50% plus one vote after the first count, second preferences will be tallied and the candidate with the greatest number of votes wins.
'Remarkable victory'
About 250,000 Sri Lankan election officials moved into position throughout the country after collecting polling cards and ballot boxes from central election offices.
Polling centres have also been set up for people displaced by the war near the northern town of Vavuniya, says the BBC's Anbarasan Ethirajan, in Colombo.
Security is tight amid fears of violence and more than 68,000 police are being deployed to protect the polling stations.
Among the early voters was President Rajapaksa.
"Today's victory will be remarkable. It's been evident with voters across the nation participating towards our victory," news agency Reuters quoted Mr Rajapaksa as saying after voting in Medamulana, his rural district on the southern coast.
"We expect a peaceful election and are getting ready to enjoy a better tomorrow."
Most voters say they are voting for peace and an improved economy.
"What I expect in the future is that in the same way peace was established, the cost of living will be brought down and the unemployment problem will be solved," Reuters quoted security guard Jayantha Perera as saying.
Hours before the polling booths opened at dawn, people in Jaffna reported hearing up to four blasts.
Acrimonious campaign
A monitoring group said two bombs were thrown at a ruling party organiser while another account said an opposition MP's home and two polling booths were targeted, the BBC's Charles Haviland reports from Colombo.
Police in Jaffna told the BBC they had no information of any trouble.
The two-month-long campaign, often marked by acrimony, officially closed on Saturday.
Election clashes have so far left four dead and hundreds wounded.
"We had in this election I think a scale of abuse of state resources which had not been registered before," news agency Reuters quoted Dr Paikiasothy Saravanamuttu, co-convenor of the Centre for Monitoring Election Violence, as saying.
But he added: "If enough Sri Lankan citizens go in large numbers as we have always done in the past and for over six decades... resisting the violence and the intimidation... then we may well get a result that at the end of the day reflects overall the wishes of the people of this country."
On Sunday, President Rajapaksa suffered a blow when ex-President Chandrika Kumaratunga vowed to back his rival.
Mrs Kumaratunga, a senior member of Mr Rajapaksa's Sri Lanka Freedom Party, said she was deeply concerned about violence, intimidation and corruption in the fiercely-contested poll.
President Rajapaksa and Gen Fonseka were closely associated with the government's defeat of the Tamil Tigers last May but the pair fell out bitterly soon after.
