Introduction: In recent decades, there has been a rise in mental illnesses. Community infrastructures are increasingly acknowledged as important for sustaining good mental health. Moreover, green spaces are anticipated to offer advantages for both mental health and social cohesion. However, the mediating pathway between green space, social cohesion and mental health and especially the proximity and characteristics of green spaces that trigger these potential effects remain of interest. Methods: We gathered data from 1365 individuals on self-reported social cohesion and mental health across four satellite districts in European cities: Nantes (France), Porto (Portugal), Sofia (Bulgaria), and Høje-Taastrup (Denmark). Green space data from OpenStreetMap was manually adjusted using the PRIGSHARE guidelines. We used the AID-PRIGSHARE tool to generate 7 indicators about green space characteristics measured in distances from 100–1500 m, every 100 m. This resulted in 105 different green space variables that we tested in a single mediation model with structural equation modelling. Results: Accessible greenness (900–1400 m), accessible green spaces (900–1500 m), accessible green space corridors (300–800 m), accessible total green space (300−800), and mix of green space uses (700–1100 m) were significantly associated with social cohesion and indirectly with mental health. Green corridors also showed negative indirect and direct associations with mental health in larger distances. Surrounding greenness and the quantity of green space uses were not associated with social cohesion nor indirectly with mental health. We also observed no positive direct associations between any green space variable in any distance to mental health. Conclusions: Our results suggest that accessibility, connectivity, mix of use and proximity are key characteristics that drive the relationship between green spaces, social cohesion and mental health. This gives further guidance to urban planners and decision-makers on how to design urban green spaces to foster social cohesion and improve mental health.