Current image fusion methods struggle to address the composite degradations encountered in real-world imaging scenarios and lack the flexibility to accommodate user-specific requirements. In response to these challenges, we propose a controllable image fusion framework with language-vision prompts, termed ControlFusion, which adaptively neutralizes composite degradations. On the one hand, we develop a degraded imaging model that integrates physical imaging mechanisms, including the Retinex theory and atmospheric scattering principle, to simulate composite degradations, thereby providing potential for addressing real-world complex degradations from the data level. On the other hand, we devise a prompt-modulated restoration and fusion network that dynamically enhances features with degradation prompts, enabling our method to accommodate composite degradation of varying levels. Specifically, considering individual variations in quality perception of users, we incorporate a text encoder to embed user-specified degradation types and severity levels as degradation prompts. We also design a spatial-frequency collaborative visual adapter that autonomously perceives degradations in source images, thus eliminating the complete dependence on user instructions. Extensive experiments demonstrate that ControlFusion outperforms SOTA fusion methods in fusion quality and degradation handling, particularly in countering real-world and compound degradations with various levels.