My brother is stealing money from me to fuel his addiction. Who should I tell?

Tell parents, doctor. This is a difficult situation. For sure "enabling" your brother is not going to solve the problem. Please consider discussing it with your parents, and your brother's clinician; although the clinician may not be able to disclose your brother's medical information to you, he/she can receive an information from you. Addiction is a disease. When treated, it often responds well to therapy.
Your brother. Tell him you dont appreciate it. You should be emotionally supportive, but not financially. I wouldn't let him in your house to have access to anything he can steal. Make it clear he will be held accountable for stealing, and if you do no press charges, you are supporting his addication. He should be accountable for his actions.