It is widely accepted that the achievement of the 17 Sustainable Development Goals (SDGs) depends on effective governance arrangements. However, it is less clear which modes and aspects of governance are important for which of the 17 goals. Until now, empirical research has mostly studied individual cases, with comparative studies largely missing. Here, we conduct a comparative analysis among 41 high and upper-middle income countries for the year 2015, drawing on the Sustainable Governance Indicators, the Global SDG Indicators Database and other official sources. Using multiple regression, we test the influence of different aspects of governance, namely participation, policy coherence, reflexivity, adaptation and democratic institutions on SDG achievement at the national level, controlling for the effects of additional socio-economic conditions. Of the tested factors, democratic institutions and participation as well as economic power, education and geographic location serve to explain SDG achievement.