The European Union is likely to introduce among the first, and most comprehensive AI regulatory regimes of the world’s major jurisdictions. We ask whether the EU’s upcoming regulation for AI will diffuse globally, producing a so-called “Brussels Effect”. 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. A de facto effect is particularly likely to arise in large US tech companies with “high-risk” AI systems. The upcoming regulation might be important in offering the first operationalisation of developing and deploying trustworthy AI.