Climate action to achieve the Paris Agreement ambitions should also respect the broader UN Sustainable Development Goals. Using an integrated assessment modelling framework with 9 harmonised models, we quantify the impacts of decarbonisation pathways on SDGs in Europe, at continental and national levels. Current climate policies would improve energy- and carbon-related aspects of sustainability (represented by metrics within SDGs 7, 9, 11, 12, and 13), inequalities (metrics within SDGs 1 and 10), and education levels (metrics within SDG 4). More ambitious net-zero emissions pathways would further improve health and agricultural productivity (metrics within SDGs 2 and 3). Furthermore, countries currently lagging in SDG performance would see the greatest benefits from ambitious climate action. Negative socioeconomic impacts from climate action (represented by metrics within SDGs 1, 2, and 8) require remedial policies, notwithstanding that our analysis does not quantify the damages that less ambitious climate policy could do to societies and the SDG Agenda.