In the architectural exterior design domain, design intent is usually expressed by textual design intent [e.g., client needs, architectural language (AL)] and non-verbal design intent (e.g., sketch). However, existing generative AI-based methods for automated architectural exterior conceptual design can only use the general image description as the prompt. Thus, despite its potential, existing generative image AI cannot produce appropriate design alternatives that meet various design requirements. Enabling automated architectural exterior conceptual design requires solving two problems: teaching the AI model to understand textual design intent and allowing generative AI to combine textual design intent with non-verbal design intent. The study aims to propose an automated architectural exterior conceptual design approach by incorporating domain-specific prompting strategies and sketch-to-image synthesis into fine-tuned generative image AI models. In the proposed approach, textual design intent annotations (including client needs and AL) are added to architectural images and general image description annotations. Web crawler and ChatGPT automatically extract design intent-related annotations from online sources for famous architectural works that are used as training images. The constructed dataset is then used to fine-tune a generative AI model [i.e., Stable Diffusion (SD)] via the Lora algorithm, teaching the AI model to understand textual design intent. Also, ControlNet is used to control the generation process of the SD model to enable the generative AI to reflect the design intent expressed by the sketches. The proposed approach is validated by comparing generated images from our approach with those from two existing models. The results show that the proposed method can successfully generate architectural exterior conceptual design images that fulfil the requirements based on the architectural design intent. The proposed approach is expected to streamline and facilitate time-consuming and demanding iterative processes during a conceptual design phase.