The Basque outfit confirmed the news via their official website.
The 22-year-old spent the past few seasons with Real Madrid Castilla after coming up through the Blancos' academy. He made his senior debut last season and trained with Real's A-team but didn't appear to have much of a future in the Spanish capital.
Alaves and Real have an excellent working relationship, with Marcos Llorente spending the 2016-17 season with El Glorioso on loan. While Zidane's move is a permanent transfer, it's likely there's a buy-back clause involved, as Los Blancos tend to include those in the majority of their deals.
The Basques enjoyed an excellent 2016-17 La Liga campaign, finishing in ninth place, and have a great reputation for nurturing talent and letting youngsters play heavy minutes.