Tebboune and other top brass attended the swearing-in ceremony alongside his defeated rivals for the presidency.
Algeria's 12-member Constitutional Council met Wednesday to confirm a presidential vacuum in the country after Abdelaziz Bouteflika announced his resignation.
Hundreds of Algerians took to the streets of the capital late on Tuesday to celebrate the departure of President Abdelaziz Bouteflika.
Bouteflika will resign before his mandate ends on April 28, state news agency APS said on Monday.
Algeria's army chief repeated a proposal on Saturday to declare President Abdelaziz Bouteflika unfit for office under article 102.
The protests had been expected to swell further after Friday prayers, as has happened on the four previous Fridays during this wave of demonstrations that kicked off on Feb 22.
When uprisings swept the region in 2011, Algeria used a heavy security and oil money to curtail demonstrations.
Algerian President Abdelaziz Bouteflika returned home on Sunday after spending two weeks in a Swiss hospital.
Algeria's President Abdelaziz Bouteflika, facing mass protests against his decision to stand for another term despite ill health
Algerian President Abdelaziz Bouteflika will run in April's elections with an offer to step down after a year if he is re-elected.
Algeria's President Abdelaziz Bouteflika sacked his tourism minister Sunday days after he was appointed to the post.
Algerians go to the polls on Thursday to elect a new parliament amid concerns that a low turnout will mar a vote