Public urban green spaces are important for the urban quality of life. Still, comprehensive open data sets on urban green spaces are not available for most cities. As open and globally available data sets the potential of Sentinel-2 satellite imagery and OpenStreetMap (OSM) data for urban green space mapping is high but limited due to their respective uncertainties. Sentinel-2 imagery cannot distinguish public from private green spaces and its spatial resolution of 10 meters fails to capture fine-grained urban structures, while in OSM green spaces are not mapped consistently and with the same level of completeness everywhere. To address these limitations we propose to fuse these data sets under explicit consideration of their uncertainties. The Sentinel-2 derived Normalized Difference Vegetation Index was fused with OSM data using the Dempster-Shafer theory to enhance the detection of small vegetated areas. The distinction between public and private green spaces was achieved using a Bayesian hierarchical model and OSM data. The analysis was performed based on land use parcels derived from OSM data and tested for the city of Dresden, Germany. The overall accuracy of the final map of public urban green spaces was 95\%, which was mainly influenced by the uncertainty of the public accessibility model.