The former France under-19 midfielder, who came through the Madrid club's academy, has signed a three-year deal with the La Liga side, who came ninth last season.
He scored on his only first-team appearance for Real Madrid in their King's Cup win over Cultural Leonesa last season.
Enzo played 78 games for Real Madrid Castilla, the club's reserve team, scoring seven goals.
"Deportivo Alaves wants to welcome Enzo Zidane and wishes him the best of luck for the new season," said a statement on the Alaves official website.
(Reporting by Ken Ferris; Editing by Ian Ransom)
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