Healthier Students for Stronger Campuses Act This bill replaces a grant program for reducing and eliminating the illegal use of drugs and alcohol on college campuses with a grant program for preventing and addressing the effects of substance use on college campuses. Specifically, it authorizes the Department of Education and the Department of Health and Human Services to award substance misuse prevention and treatment grants to institutions of higher education (IHEs) with regional high incidences of substance use disorders, overdoses, and deaths. It requires at least 25% of funds to be awarded to IHEs in rural areas. The bill requires IHEs to use funds for evidence-based or promising interventions designed to address and prevent substance use disorders among enrolled students, such as recovery services, treatment or referral to treatment, and mental health counseling. IHEs receiving such grants must provide at least a 20% match of nonfederal funds.