Election officials estimated more than 65-70 per cent voting in most places in the first 7 hours of voting.
There were no major reports of violence, although private monitoring group the Campaign for Free and Fair Elections said some voters had been prevented from voting that ended at 4 pm local time.
"We hope to announce the first postal vote result by 10 pm tonight," Mahinda Deshapriya, the Commissioner of Elections, said.
Some 1,586,598 of the country's 21 million population are eligible to vote. About 1,076 polling stations were set for elections.
There are 19 candidates in the fray. But the main fight is between two-term president 69-year-old Rajapaksa and his 63-year-old former cabinet colleague Sirisena.
Long queues were seen outside the polling stations around the country.
"There is heavy polling everywhere," Keerthi Tennakoon of Campaign for Free and Fair Elections said.
"We will have a resounding victory. That is very clear. From tomorrow, we will start implementing our manifesto," he told reporters in his constituency in Hambantota.
Voters from minority Tamil community turned out to vote in large numbers in the areas dominated by them, defying intimidation attempts.
In the three northern districts of Tamil regions in Jaffna, Kilinochchi and Mullaithivu over 50 per cent polling was recorded.
In some Muslim dominated areas, mosques' loudspeakers were used by the community members to encourage voters to cast their votes.
"People are keen to vote, there were several hundreds already queuing up when the poll stations opened," said E Saravanabhavan, a Tamil parliamentarian from Tamil National Alliance.
Tennakoon said that there was remarkable enthusiasm in the Muslim dominated Puttalam in the north western province.
"In a polling station for 1,200 voters, 800 of them finished voting in the first hour," Tennakoon said.
The Tamils angered by Rajapaksa's successful military campaign that crushed the LTTE were expected to favour his rival, the opposition unity candidate, Sirisena.
Opposition had complained to the international polls monitoring groups of a plot by the military to deter Tamils from voting.
Monitors said a hand grenade was thrown at an abandoned house located near by a polling center in Alwai, Point Pedro in the Jaffna peninsula. No casualties were reported.
There was also a hand grenade explosion nearer to a polling station at Nelukkulama in the northern district of Vavuniya. Police said no one was hurt.
In the main towns in the southern parts of the island the turn out had exceeded 50 per cent in most main areas, election officials said. The central district of Kandy had recorded the highest turn-out of 60 per cent by 12 noon followed by the capital district Colombo with over 50 per cent poll.
Rajapaksa and his family voted in the home base of Hambantota while his challenger Sirisena voted in the north central provincial town of Polonnaruwa.
Deshapriya, the elections chief, was keen to ensure a free and fair poll. He visited the offices of the state television, Rupavahini to demand a correction of a news story concerning an opposition front liner.
Rajapaksa had called the election two years ahead of schedule, hoping to win a record third six-year term before the defeat of the Tamil Tigers fades in the memory of the people of the island which saw a three decades war over the demand of a separate Tamil Eelam.
The veteran politician was taken by surprise by the candidacy of former health minister, Sirisena, who walked out of the government a day after polls were called. That set off a wave of political turmoil and energised a long-dispirited opposition that had not been looking forward to the election.
Both the president and his challenger belong to the majority Sinhala Buddhist community and much depends on how the minorities Tamils and Muslims vote in the elections.
President Rajapaksa has been the undisputed leader of the country for nearly a decade. But Sri Lanka is still grappling with divisions between the Sinhalese majority and Tamil minority groups.
Grievances for Tamils include the continuing heavy presence of the Sri Lankan army in northern areas and a lack of local political autonomy.
The biggest Tamil political grouping has endorsed Sirisena's candidacy. Muslim parties concerned by rising violence from a range of hardline Buddhist groups which have emerged in recent years have also joined the opposition.
The opposition campaign accuses Rajapaksa of nepotism, misrule, corruption and authoritarianism.
Rajapaksa's brothers -- Gotabhaya and Basil -- are defence and economic ministers respectively besides a number of his family members who are holding key posts and positions.
Sirisena backed by the main opposition United National Party and another key breakaway group the JHU or the Buddhist Monk party have plans for a series of constitutional and democratic reforms.