This article studies regional income convergence and its conditioning factors in 267 subnational regions of the European Union during the 2003–2016 period. Building on previous research that documents the formation of multiple convergence clubs in per-capita income, we study the role of structural change and spatial dependence as key conditioning factors of the club convergence process. Our results are threefold. First, we document that the spatial distribution of the convergence clubs shows a strong degree of spatial dependence. Second, when we study the evolution of structural change and spatial dependence, our results show that the share of manufacturing has been decreasing, while its degree of spatial dependence has been increasing over time. In contrast, the share of knowledge-intensive services has increased, while its degree of spatial dependence has decreased. Third, we evaluate the role of structural change and spatial dependence in the formation of convergence clubs using a spatial ordered-logit model. Our results show that when spatial dependence is omitted from the econometric specification, both manufacturing and knowledge-intensive services are not significant predictors of club convergence. Only when spatial dependence is added to the specification do most of the structural change variables become statistically significant. In addition, there are contrasting spatial effects between variables of structural change. On the one hand, the geographical spillover effects for manufacturing and routine services are statistically significant. On the other hand, knowledge-intensive services do not show significant spatial spillover effects. Overall, our results highlight the joint importance of structural change and spatial dependence in the formation of convergence clubs. Specifically, the notion of spatial structural change deserves further attention, as it appears to play a major role in the evolution of regional disparities in the European Union.