The 2030 Agenda with its Sustainable Development Goals (SDGs) and the Paris Agreement on climate change were adopted in 2015. Although independently defined, the two agreements are strongly interlinked. We developed a framework that scores the impacts of climate-change actions on all SDG targets based on directionality (i.e., trade-offs or co-benefits) and likelihood of occurrence (i.e., ubiquitous or context-dependent), and categorizes them by dependence on four key context dimensions—geographical, governance, time horizon and limited natural resources. Through an extensive literature review, we found that climate-change mitigation measures directly affect most SDGs and their targets, mostly through co-benefits. Improving energy efficiency, reducing energy-services demand and switching to renewables provide the most co-benefits. In contrast, carbon capture and storage and nuclear energy likely lead to multiple trade-offs. We show how understanding the relevant context dimensions facilitates policy design and policy mixes that enhance co-benefits and minimize trade-offs. Finally, by assessing the prevalence of climate-change mitigation measures in G20 countries, we found that measures with more co-benefits are more frequently adopted. Our study advances the knowledge of climate–SDG interactions, contributing to climate and sustainable development governance research, and facilitating policy design for a joint implementation of the Paris Agreement and the 2030 Agenda.