The 74-year-old succeeds Abdelaziz Bouteflika, who was forced to resign in April after two decades in power.
Tebboune took 58 per cent of the votes in Thursday's election, on the basis of figures released by the country’s electoral commission.
Tebboune and the four other candidates were criticised for being closely linked with the former president Bouteflika, who stepped down following interminable massive demonstrations.
Anti-government rallies have continued, however, with protesters demanding the sweeping away of the entire political establishment.
Thousands of people took to the streets of the capital, Algiers, on Thursday to protest against the election.
Tebboune served as housing minister under President Bouteflika and then had a brief spell as prime minister.
Electoral officials say about nine million people voted - a turnout of about 40 per cent.
"The turnout is satisfying and it will give the new president enough backing to implement his reforms," said Ahmed Mizab, a commentator on state television.