"FIFA officially granted... goalkeeper Luca Zinedine Zidane authorisation to represent the Algerian national team," FAF said in a statement.
FIFA's "change of association platform" showed the decision was dated on Friday.
Luca Zidane represented France at youth levels and currently plays for Granada in Spain's second division.
Since he never made the step up to the French national team, he remained eligible to play for Algeria, the country of his paternal grandparents.
The North Africans have qualified for the 2025 African Cup of Nations, set to begin on December 21 in Morocco. They are also leading their World Cup qualifying Group G with 19 points, needing either a win against Somalia or a draw with Uganda next month to qualify for the 2026 World Cup.
Zidane also played for Real Madrid's reserve team after working his way up from its youth academy, which he joined in 2004.
He debuted with the main team in their last league game in the 2017-2018 season and was the third-choice goalkeeper when Real won their 13th Champions League title in 2018.
Although Zinedine Zidane was born in Marseille, his family was originally from a small village in Bejaia, some 250 kilometres east of Algiers.
