How can an older sibling get legal guardianship/Custody of a younger sibling?

My mom is moving out of town but I live in my own apartment here; I’m 20 years old and my 16-year-old brother would like to continue going to the same schools in this town but if our mom moves he would have to move schools. My mom wants to give me permission to let him live with me while he finishes out high school so that he can stay in the same school. How do I go about allowing him to live with me and become his guardian.