He was previously with Glasgow's EDP group and played club rugby with Hawks.
Zander, a product of Dundee High School and Strathallan School made his Warriors debut off the bench against Benetton Treviso in October.
The 19-year-old was invited to train with the Scotland squad during last November's viagogo Autumn Tests. He scored the winning try for Scotland under-20s in their victory over Wales last month and was named man of the match when Scotland under-20s defeated Italy 45-0.
Zander told glasgowwarriors.org: "This is a fantastic opportunity for me to continue my development and I'm very happy to sign my first professional contract with the club.
"The last few months have been an incredible learning curve for me and now I've signed this deal I'm determined to work hard and make the most of the chance I've been given."