Modern manufacturing demands robotic assembly systems with enhanced flexibility and reliability. However, traditional approaches often rely on programming tailored to each product by experts for fixed settings, which are inherently inflexible to product changes and lack the robustness to handle variations. As Behavior Trees (BTs) are increasingly used in robotics for their modularity and reactivity, we propose a novel hierarchical framework, Video-to-BT, that seamlessly integrates high-level cognitive planning with low-level reactive control, with BTs serving both as the structured output of planning and as the governing structure for execution. Our approach leverages a Vision-Language Model (VLM) to decompose human demonstration videos into subtasks, from which Behavior Trees are generated. During the execution, the planned BTs combined with real-time scene interpretation enable the system to operate reactively in the dynamic environment, while VLM-driven replanning is triggered upon execution failure. This closed-loop architecture ensures stability and adaptivity. We validate our framework on real-world assembly tasks through a series of experiments, demonstrating high planning reliability, robust performance in long-horizon assembly tasks, and strong generalization across diverse and perturbed conditions. Project website: https://video2bt.github.io/video2bt_page/