Algeria's president has signed the country's new constitution into law, his office said.

The document was approved in a November referendum on record low turnout as its leader received treatment abroad for COVID-19.

President Abdelmadjid Tebboune, who returned to Algeria this week after two months in Germany, had promoted the new constitution as the "cornerstone of the new Algeria", as he sought to turn the page on the long-running Hirak mass protest movement.

But the document received the backing of less than 15 per cent of the electorate, in a November vote overshadowed by the novel coronavirus pandemic and following Hirak calls for a boycott.

The Hirak first launched vast street demonstrations in early 2019 to oppose then-president Abdelaziz Bouteflika's bid for a fifth term in office. 

Following his resignation that April, the Hirak kept up the pressure to demand a full overhaul of the ruling system in place since the North African country's 1962 independence from France.

The new constitution was pitched as responding to the demands of the Hirak, but keeps in place Algeria's presidential regime and expands the powers of the army, a central pillar of the state.

Tebboune, 75, on Thursday approved Algeria's 2021 budget and is hoping to launch a vaccination campaign against the novel coronavirus, using the Sputnik V jab produced by its Russian ally, as early as this month.