No details of the 50-year-old's contract terms were announced by the Algerian Football Federation on Thursday.
Alcaraz, who has also worked at Levante and Elche, takes over from Belgian George Leekens who quit after Algeria’s early exit from the African Nations Cup finals in Gabon in January.
Alcaraz’s third term as manager at Granada ended on Monday after their weekend loss at home to Valencia left them second-from-bottom in La Liga. He has been replaced by former England defender Tony Adams.
His first match in charge for Algeria will be in June against Togo at the start of the 2019 Nations Cup qualifiers.