Vision-Language Models (VLMs) have been widely used in various visual recognition tasks due to their remarkable generalization capabilities. As these models grow in size and complexity, fine-tuning becomes costly, emphasizing the need to reuse adaptation knowledge from 'weaker' models to efficiently enhance 'stronger' ones. However, existing adaptation transfer methods exhibit limited transferability across models due to their model-specific design and high computational demands. To tackle this, we propose Transferable Model-agnostic adapter (TransMiter), a light-weight adapter that improves vision-language models 'without backpropagation'. TransMiter captures the knowledge gap between pre-trained and fine-tuned VLMs, in an 'unsupervised' manner. Once trained, this knowledge can be seamlessly transferred across different models without the need for backpropagation. Moreover, TransMiter consists of only a few layers, inducing a negligible additional inference cost. Notably, supplementing the process with a few labeled data further yields additional performance gain, often surpassing a fine-tuned stronger model, with a marginal training cost. Experimental results and analyses demonstrate that TransMiter effectively and efficiently transfers adaptation knowledge while preserving generalization abilities across VLMs of different sizes and architectures in visual recognition tasks.