Visual In-Context Learning (ICL) has emerged as a promising research area due to its capability to accomplish various tasks with limited example pairs through analogical reasoning. However, training-based visual ICL has limitations in its ability to generalize to unseen tasks and requires the collection of a diverse task dataset. On the other hand, existing methods in the inference-based visual ICL category solely rely on textual prompts, which fail to capture fine-grained contextual information from given examples and can be time-consuming when converting from images to text prompts. To address these challenges, we propose Analogist, a novel inference-based visual ICL approach that exploits both visual and textual prompting techniques using a text-to-image diffusion model pretrained for image inpainting. For visual prompting, we propose a self-attention cloning (SAC) method to guide the fine-grained structural-level analogy between image examples. For textual prompting, we leverage GPT-4V's visual reasoning capability to efficiently generate text prompts and introduce a cross-attention masking (CAM) operation to enhance the accuracy of semantic-level analogy guided by text prompts. Our method is out-of-the-box and does not require fine-tuning or optimization. It is also generic and flexible, enabling a wide range of visual tasks to be performed in an in-context manner. Extensive experiments demonstrate the superiority of our method over existing approaches, both qualitatively and quantitatively.