The progress of autonomous web navigation has been hindered by the dependence on billions of exploratory interactions via online reinforcement learning, and domain-specific model designs that make it difficult to leverage generalization from rich out-of-domain data. In this work, we study data-driven offline training for web agents with vision-language foundation models. We propose an instruction-following multimodal agent, WebGUM, that observes both webpage screenshots and HTML pages and outputs web navigation actions, such as click and type. WebGUM is trained by jointly finetuning an instruction-finetuned language model and a vision encoder with temporal and local perception on a large corpus of demonstrations. We empirically demonstrate this recipe improves the agent's ability of grounded multimodal perception, HTML comprehension, and multi-step reasoning, outperforming prior works by a significant margin. On the MiniWoB, we improve over the previous best offline methods by more than 45.8%, even outperforming online-finetuned SoTA, humans, and GPT-4-based agent. On the WebShop benchmark, our 3-billion-parameter model achieves superior performance to the existing SoTA, PaLM-540B. Furthermore, WebGUM exhibits strong positive transfer to the real-world planning tasks on the Mind2Web. We also collect 347K high-quality demonstrations using our trained models, 38 times larger than prior work, and make them available to promote future research in this direction.