The prevalence of depression is a major societal health concern, and there is an ongoing need to develop tools that predict who will become depressed. Past research suggests that depression changes the language we use, but it is unclear whether language is predictive of worsening symptoms. Here, we test whether the sentiment of brief written linguistic responses predicts changes in depression. Across two studies (N = 467), participants provided responses to neutral open-ended questions, narrating aspects of their lives relevant to depression (e.g., mood, motivation, sleep). Participants also completed the Patient Health Questionnaire (PHQ-9) to assess depressive symptoms and a risky decision-making task with periodic measurements of momentary happiness to quantify mood dynamics. The sentiment of written responses was evaluated by human raters (N = 470), Large Language Models (LLMs; ChatGPT 3.5 and 4.0), and the Linguistic Inquiry and Word Count (LIWC) tool. We found that language sentiment evaluated by human raters and LLMs, but not LIWC, predicted changes in depressive symptoms at a three-week follow-up. Using computational modeling, we found that language sentiment was associated with current mood, but language sentiment predicted symptom changes even after controlling for current mood. In summary, we demonstrate a scalable tool that combines brief written responses with sentiment analysis by AI tools that matches human performance in the prediction of future psychiatric symptoms.