The development of AI for mental health is hindered by a lack of authentic therapy dialogues, due to strict privacy regulations and the fact that clinical sessions were historically rarely recorded. We present an LLM-driven pipeline that generates synthetic counseling dialogues based on structured client profiles and psychological questionnaires. Grounded on the principles of Cognitive Behavioral Therapy (CBT), our method creates synthetic therapeutic conversations for clinical disorders such as anxiety and depression. Our framework, SQPsych (Structured Questionnaire-based Psychotherapy), converts structured psychological input into natural language dialogues through therapist-client simulations. Due to data governance policies and privacy restrictions prohibiting the transmission of clinical questionnaire data to third-party services, previous methodologies relying on proprietary models are infeasible in our setting. We address this limitation by generating a high-quality corpus using open-weight LLMs, validated through human expert evaluation and LLM-based assessments. Our SQPsychLLM models fine-tuned on SQPsychConv achieve strong performance on counseling benchmarks, surpassing baselines in key therapeutic skills. Our findings highlight the potential of synthetic data to enable scalable, data-secure, and clinically informed AI for mental health support. We will release our code, models, and corpus at https://ai-mh.github.io/SQPsych