Tebboune, 74, received 58.15% of the vote in this North African country, according to the head of the National Independent Electoral Authority, Mohamed Charfi. Turnout was just 41%, reflecting the frustration of many Algerians who hoped to see new faces among the candidates.
Tebboune served briefly as prime minister in 2017 under ex-President Abdelaziz Bouteflika, who was ousted in April by peaceful protests that have been called Algeria's Arab Spring. The election of Tebboune, an establishment figure, disappointed protesters who believe the poll was rigged in favor of the old regime.
Tebboune is reportedly close to powerful army chief Gaid Salah, a much-criticized figure among members of the protest movement that began in February. They seek fresh elections, new leadership and an end to corruption.
Tens of thousands of protesters on Friday demanded a "free and democratic" Algeria and rejected the vote results, chanting "No to elections of shame" and denouncing suspected fraud.
The largely peaceful marches took place in the capital, Algiers, as well as Oran, Constantine and other cities. Some were quickly dispersed by police. Algerian media reported numerous arrests.
Algeria is one of the most youthful countries in the world, with two-thirds of the population under 30. A quarter of those youth are out of work, leading to discontent with the country's veteran rulers and the opaque policies that have left them behind.
The electoral authority was recently created in an attempt at transparency in a nation where leaders have been thought to be chosen in advance by the elite.
This election's low turnout compares to the nearly 52% in 2014, when Bouteflika won with 81% of the vote.
Former minister Abdelkader Bengrina came in second in Thursday's vote with 17%, with former Prime Minister Ali Benflis third with 10%.
The president-elect, who endured insults and protests during the 22-day campaign, has already suffered setbacks. The man in charge of Tebboune's campaign financing, Omar Alilat, has been jailed on corruption charges. And Tebboune's son will be questioned Dec. 5 in a drug case, according to Algeria's national television.
Tebboune held ministerial posts in successive Bouteflika governments, responsible for issues including communications and urbanism. He was prime minister between May and August 2017 but was fired by Said Bouteflika, the ex-president's younger brother, who was convicted in September on corruption charges and is serving 15 years in prison. Tebboune reportedly made decisions that ran counter to powerful businessmen in Bouteflika's entourage who are now in prison for graft.
Tebboune during his campaign tried to put forward an image of a man who went after oligarchs in Said Bouteflika's circle, but he had a hard time making voters forget his ties to the Bouteflika clan.
For two decades, Algeria was ruled by Bouteflika and other survivors of the 1954-1962 War of Independence against colonial power France.
French President Emmanuel Macron on Friday refrained from congratulating Algeria's president-elect, instead saying that "I simply wish the aspirations Algerian people expressed are answered in a dialogue that must open between authorities and the population."
Macron added that "it's Algerians' responsibility to find the ways and means in the context of a real democratic dialogue."