In several districts in the capital voting was delayed for up to two hours as people waited for the polls to open.
During the campaign, Ali Bongo has pledged change in the impoverished West African nation, while also defending the legacy of his father, who had been widely accused of corruption.
"It's not contradictory - not at all," he said as he attended his final campaign rally on Saturday.
"How could I not be confident?" Bongo asked, pointing at the thousands of supporters chanting his name.
Gabon is sub-Saharan Africa's fourth biggest oil producer, the world's third biggest provider of manganese and Africa's second biggest wood exporter, but an estimated 60 per cent of the population lives below the poverty line.
Bongo and the other frontrunners - Andre Mba Obame, Casimir Oye Mba and Pierre Mamboundou - have all promised a fairer distribution of the country's natural resources.
A total of 23 politicians were originally in the race, but on Friday representatives of five candidates, including Jean Eyeghe Ndong, a former prime minister, Paul Mba Abessole, a former opposition leader, decided to stand down in favour of Obame, a former interior minister.
But the announcement also caused a row with four other contenders, including Oye Mba, a former oil minister, denying claims that they had joined the other candidates in pulling out of the race.
Many candidates have questioned the electoral roll, saying that the official figure of 813,164 eligible voters in a country of 1.5 million was too high.
However, Adama Gaye, an Africa analyst based in Senegal, said that the election was likely to be the most open in Gabon's history.
"President Bongo was not just Africa's longest-serving president, but also the world's longest-serving president," he told Al Jazeera.
"Because of his really high stature and financial muscle the elections were usually a foregone conclusion and there was also support from the French authorities to ensure he won."
More than 300 observers have been accredited for the vote, including representatives from the African Union, the Organisation of the Islamic Conference and a global grouping of francophone countries.
There are also fears that lingering anger over the huge personal fortune accumulated by Omar Bongo will prompt unrest if Ali Bongo wins.
Al Jazeera's Adow said that the opposition candidates had warned that they would "not take an Ali Bongo victory lying down".
"Despite all the security in the capital, many people have been leaving the city and heading to their rural homes," he said.
A group of leading intellectuals in Gabon on Saturday urged all sides not to resort to violence after the election, pointing to "numerous worrying signals" and warning of "confrontations" in the wake of the vote.
Before the polls opened, Bongo issued a warning to any potential protesters.
"It is clear that we cannot accept disorder... We shall use all the institutions that the law authorises us to use - the street belongs to no one," he told Radio France International.
The 3,000 polling stations across the country have been placed under heavy security and voters have been told to return to their homes after voting.