Madjer, 58, becomes the country’s fifth national coach in three years and must pick up the pieces after their failure to qualify for the 2018 World Cup.
That cost Spaniard Alcaraz his position as he was sacked earlier this month after just six months in the role.
Madjer, one of the greatest Algerian players of all time, is best remembered for his nonchalant back-heeled finish for Porto in their 1987 European Cup final win over Bayern Munich.
He first took charge of his country in 1994, with his most recent spell ending in 2002 after an early exit from that year’s Africa Cup of Nations.
Madjer’s aim on his return to the helm will be to take the team to the 2019 Cup of Nations in Cameroon, with their next qualifier due to be against Gambia in March.
Before that, they must complete their failed World Cup campaign with a fixture against Nigeria next month.