Limited access to mental healthcare resources hinders timely depression diagnosis. Social media platforms present a valuable data source for early detection, yet this task faces two significant challenges: 1) the need for medical knowledge to distinguish clinical depression from transient mood changes, and 2) the dual requirement for high accuracy and model explainability. To address this, we propose DORIS, a framework that leverages Large Language Models (LLMs). To integrate medical knowledge, DORIS utilizes LLMs to annotate user texts against established medical diagnostic criteria and to summarize historical posts into temporal \textit{mood courses.} These medically-informed features are then used to train an accurate Gradient Boosting Tree (GBT) classifier. Explainability is achieved by generating justifications for predictions based on the LLM-derived symptom annotations and mood course analyses. Extensive experimental results validate the effectiveness and interpretability of our method, highlighting its potential as a supportive tool for mental health professionals.