The reforms are meant to address longstanding public grievances in the North African nation, and possibly to prepare for a smooth transition amid concerns over the health of 78-year-old President Abdelaziz Bouteflika.
The package was passed by 499 votes to two, with 16 abstentions, Senate speaker Abdelkader Bensalah said.
It included a measure to recognise as official the Amazigh language spoken by the indigenous Berber population, alongside Arabic.
A two-term limit on the presidency -- lifted in 2008 to allow Bouteflika to run for a third time -- will be reintroduced and the president will be required to nominate a prime minister from the largest party in parliament.
Bouteflika -- whose public engagements have become rare since suffering a stroke in 2013 -- will be allowed to finish his fourth term, which ends in 2019, and run for a fifth if he wishes.
The package also prevents Algerians with dual nationality from running for high posts in public office, which has sparked criticism among the Franco-Algerian community.
It foresees the creation of an independent electoral commission and recognition of the roles of women and youth. Freedoms of assembly and the press will be explicitly guaranteed.
After the vote, Prime Minister Abdelmalek Sellal hailed the president as "the architect of the new Algerian republic".
But critics disagree, saying the reforms are little more than a show and will do little to reduce the influence of the powerful elite, including Bouteflika's National Liberation Front party and army generals.
'Constitutional power grab'
Former lawmaker and regime opponent Djamel Zenati said that "with the current revision, our country's constitution finally brings together the main elements necessary to build a democracy".
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But as "violating laws has become the law" in Algeria, it is hard to believe those in power are being even "the slightest bit sincere", he wrote in El Watan newspaper.
Former prime minister Ali Benflis, who was Bouteflika's rival in the 2014 presidential polls, slammed the reforms as a "constitutional power grab" to "solve only the regime's -- not the country's -- problems".
The president and his supporters have moved in recent months to take control of the security services, dissolving the powerful Department of Intelligence and Security and jailing or sidelining top officials.
Bouteflika and his inner circle have held a firm grip on power since 1999 and, as the end of his rule appears to close in, there are fears of instability in the mainly Muslim country of 40 million, a key energy producer.
"This project crowns the process of political reforms promised by the head of state," Sellal told parliamentarians.
The reforms guaranteed "democratic change by means of free elections" and were "a bulwark against the vagaries of political change," he said, referring to parts of the constitution that cannot be altered if Islamists form a majority.
Unlike many countries in the region, including its neighbours Libya and Tunisia, Algeria has been relatively stable since the 2011 Arab Spring.
But it is facing a range of challenges, including regular jihadist attacks, sporadic outbreaks of violence between Berbers and Arabs, and a precipitous drop in state revenues as oil prices have plummeted.
The High Council of the Amazigh affairs (HCA), set up in 1995 to promote teaching the Berber tongue in public schools, has welcomed the Berber language becoming official.
It will allow "the state to dedicate more means and measures to make up for shortcomings", HCA secretary-general Si El Hachemi Assad said.
Around a fourth of Algerians speak regional variants of Amazigh, but less than 3 percent of students learn it at school, the HCA says.
Algeria hopes to create an Amazigh language academy to address its standardisation and transcription into one of the Berber, Latin or Arabic alphabets.