07:38 GMT - Widodo's Indonesian Democratic Party of Struggle (PDI-P) is declaring victory for their presidential candidate.
07:17 GMT - Prabowo, who ramped up his nationalistic rhetoric in the last weeks of his campaign, tells reporters after casting his vote: "I will respect the people's decision, but it must be really their decision and not an engineered one. If it's engineered, we must take clear action. But I'm optimistic that the organisers can ensure a good process."
07:15 GMT - A series of "quick counts", which are unofficial tallies from polling agencies, shows Widodo leading with around 53 percent against Prabowo's 47 percent.
07:09 GMT - Widodo leads - Pollsters are saying Widodo is in the lead after a series of "quick counts".
07:06 GMT - A couple inks their fingers after voting
07:03 GMT - Several months ago a Widodo win was regarded almost as a foregone conclusion with some surveys giving him a lead of 30 percentage points over Prabowo.
But the final opinion polls before voting gave him a lead of just 2.7 percentage points according to the survey from Saiful Mujani Research and Consulting, with large numbers of voters undecided. The firm warned the gap between the two is so narrow that there is a "potential for cheating" and that democracy "could collapse", adding that: "The worst scenario is chaos."
06:37 GMT - Widodo supporters celebrate - Our correspondent Arlina Arshad is outside the house of Megawati Sukarnoputri, the head of Widodo's Indonesian Democratic Party of Struggle (PDI-P), in south Jakarta.
Widodo is expected to arrive soon and there are some 300 supporters and journalists waiting outside. The atmosphere is festive, with vendors selling colourful balloons and musicians playing instruments to greet him. Some are wearing masks of bull faces -- the symbol of the PDI-P.
Whenever a vehicle comes close, the crowds start shouting "Jokowi!"
06:35 GMT - Papuan tribesmen at a voting center in Jayapura
06:32 GMT - The new leader will have to contend with rampant corruption, slowing economic growth, millions mired in poverty, and mounting fears that Islamic radicals returning from Middle East conflicts could revive militant networks.
06:18 GMT - Voting has now closed and a series of "quick counts" by pollsters begins. These are expected to give an accurate indication of the winner but official results are not expected for about two weeks.
For transparency, counters hold up ballots one by one and yell out each vote, while other counters tally the results on a large sheet displayed for the public to see.
Whoever wins will be the country's second directly-elected president after Yudhoyono, who steps down in October after a decade of stable but often indecisive rule.
06:16 GMT - Indonesian presidential candidate Prabowo Subianto
06:14 GMT - Our reporters say several remote districts in Papua province were still waiting to receive ballot boxes and papers when voting opened this morning, after days of heavy rain and winds prevented aircraft from making deliveries.
Katharina Utomo, a 38-year-old housewife, was the first to vote at a polling station in the Papuan capital, Jayapura, weary from watching a World Cup football match in the early morning. "I voted for Jokowi because I think he's made himself close to the people and he also came here to Papua to campaign," she tells AFP.
Men and women from traditional tribes are also voting in Jayapura, some of the men carrying bows and arrows and wearing only the traditional penis gourd.
In South Jakarta, 33-year-old Zakaria, tells our reporter he voted for Prabowo because of his background in the military. "He must be firm in running this country. This is important because we are facing a lot of problems. He is also supported by many Muslim parties. As a Muslim, I must vote for him," he says.
06:00 GMT - Respect people's choice - President Susilo Bambang Yudhoyono calls for a peaceful and fair election, asking the candidates to accept the results.
He tells the public: "Our democracy is already mature, and our people -- each person -- have chosen freedom to choose with the right to vote. Because of this, I call on all leaders and political elite in this country to respect the choice of the people, to respect the freedom of the people to choose their leaders."
05:57 GMT - Widodo and his wife Iriana vote in Jakarta
05:54 GMT - Widodo leads - An early quick counts show Widodo in the lead, but with voting still open in central and western Indonesia, the numbers are likely to change in the coming hours.
05:45 GMT - Indonesians decide - Some 190 million voters are eligible to cast ballots across the sprawling archipelago of more than 17,000 islands that spread across three time zones.
Widodo and Prabowo vote almost simultaneously at separate stations at around 10.30 am (0330 GMT).
Widodo, dressed in a traditional, patterned Indonesian shirt and accompanied by his wife, who is wearing a Muslim headscarf, casts his vote at Taman Suropati, a park in central Jakarta.
He tells voters: "Today is the day Indonesians decide their future for the next five years."
Prabowo is escorted by two mounted policemen as he votes at a polling station near his home in the outskirts of the capital.
"I'm very optimistic, and God willing we will get support from people everywhere," he tells reporters.
05:39 GMT - A woman casts her ballot in Jakarta
05:34 GMT - Close call - A former furniture exporter Widodo, known by his nickname Jokowi, was born in a bamboo shack in a riverbank slum on Indonesia's main island of Java and is the first serious presidential contender without links to the authoritarian past.
An ex-general, Prabowo ordered the abduction of democracy activists in the dying days of dictator Suharto's rule, was once refused entry to the US over rights abuses, and used to be married to one of the strongman's daughters.
Widodo was regarded the long-time favourite to take the presidency but in recent weeks Prabowo's popularity has surged, and now opinion polls indicate the election could be much closer than once anticipated.
05:21 GMT - Indonesia votes - WELCOME TO AFP'S LIVE REPORT on Indonesia's bitterly fought presidential election -- the tightest and most divisive vote since the downfall of dictator Suharto.
Voters face a choice between two starkly different candidates and perhaps two very different paths for the world's third-biggest democracy.
The election pits Jakarta governor Joko Widodo against Prabowo Subianto, an ex-general with a chequered human rights record.