Climate action to achieve the Paris Agreement should respect the United Nations Sustainable Development Goals. Here, we use an integrated assessment modelling framework comprising nine climate policy models and quantify the impacts of decarbonisation pathways on Sustainable Development Goals in the European Union at regional and national levels. We show that scenario-consistent assumptions of future socio-economic trends and current climate policies would improve energy- and carbon-related aspects of sustainability and reduce inequalities. Ambitious net-zero emissions pathways would further improve health and agricultural productivity. Furthermore, countries currently lagging in achieving sustainable development goals would see the greatest benefits from ambitious climate action. Negative socio-economic impacts from climate action on poverty, hunger, and economic growth will require specific corrective policies. While our analysis does not quantify the negative effects of less ambitious climate policy, it demonstrates where co-benefits and trade-offs of greenhouse gas mitigation and sustainable development agenda exist and can guide policy formulation.