The vote had widely been seen as a regime maneuver to neutralize the Hirak protest movement, which at its peak had swept long-time president Abdelaziz Bouteflika from power.
The Hirak had called for a boycott of the referendum.
The revised text passed with 66.8 percent of the vote, National Independent Elections Authority (ANIE) chief Mohamed Charfi told a press conference, noting that the exercise took place in the shadow of the coronavirus pandemic.
Charfi had earlier announced turnout of just 23.7 percent, a historic low for a major vote.
The plebiscite took place in the absence of President Abdelmadjid Tebboune, who is hospitalized overseas after reported cases of the COVID-19 illness among his staff.
Tebboune had been elected in December in a poll with a turnout of just under 40 percent, the lowest in a presidential election since independence.
Said Salhi, deputy president of the Algerian Human Rights League, said the low turnout was "a victory for the Hirak."
"The regime must take note of its failure and reconsider its roadmap," he tweeted. "The process of democratic transition is the solution."
The Hirak movement, whose unprecedented mass rallies toppled Tebboune's veteran predecessor Abdelaziz Bouteflika in April 2019, had pressed on with months of mass demonstrations to demand deep reforms to the ruling system, before it suspended rallies in March to stem the spread of coronavirus.
Tebboune has pitched the tweaked constitution as meeting the movement's demands, rhetoric echoed by Charfi on Monday.