The 78-year-old president is seen as the favourite to take on his two challengers, moderate Islamist Abdelaali Hassani and Socialist candidate Yousef Ausish.
The streets of the Algerian capital were mostly quiet early on Saturday, with most voters expected to head to the polls by mid-day.
"I came early to do my duty and elect the president of my country in a democratic way," said Sid Ali Mahmoudi, a 70-year-old voter who cast his ballot early.
Polls opened at 8:00 a.m. local time and are due to close at 7:00 p.m.
Preliminary results could be announced as early as tonight, and the electoral authority ANIE will announce the official results on September 8 at the latest.
"The winner is known in advance," political commentator Mohamed Henad wrote on Facebook before voting began, referring to Tebboune.
Tebboune's opponents did not stand much of a chance due to low support and the conditions in which the election campaign, which was nothing short of a farce, was conducted," Henad wrote.
The main challenge for the incumbent president is to boost voter turnout in the North African country after he won with 58% of the vote in 2019 but amid a record abstention rate of over 60%.
"The president wants to have a significant turnout. That's his main problem," said Hasni Abidi, an analyst at the Geneva-based CERMAM Research Center.
The low turnout in 2019 followed pro-democracy protests in Herakh that ousted former president Abdelaziz Bouteflika from power before being quelled with a stepped-up police crackdown and the jailing of hundreds of people.
Presidential candidate Hassani said he also hoped for a high turnout.
"We hope that the Algerian people will vote decisively. The high turnout gives more credibility to this election," he told reporters. | BGNES