The European Union is likely to introduce among the first, most stringent, and most comprehensive AI regulatory regimes of the world’s major jurisdictions. In this report, we ask whether the EU’s upcoming regulation for AI will diffuse globally, producing a so-called “Brussels Effect”. Building on and extending Anu Bradford’s work, we outline the mechanisms by which such regulatory diffusion may occur. We consider both the possibility that the EU’s AI regulation will incentivise changes in products offered in non-EU countries (a de facto Brussels Effect) and the possibility it will influence regulation adopted by other jurisdictions (a de jure Brussels Effect). Focusing on the proposed EU AI Act, we tentatively conclude that both de facto and de jure Brussels effects are likely for parts of the EU regulatory regime. A de facto effect is particularly likely to arise in large US tech companies with AI systems that the AI Act terms “high-risk”. We argue that the upcoming regulation might be particularly important in offering the first and most influential operationalisation of what it means to develop and deploy trustworthy or human-centred AI. If the EU regime is likely to see significant diffusion, ensuring it is well-designed becomes a matter of global importance.