Climate change affects precipitation patterns. Here, we investigate whether its signals are already detectable in reported river flood damages. We develop an empirical model to reconstruct observed damages and quantify the contributions of climate and socio-economic drivers to observed trends. We show that, on the level of nine world regions, trends in damages are dominated by increasing exposure and modulated by changes in vulnerability, while climate-induced trends are comparably small and mostly statistically insignificant, with the exception of South & Sub-Saharan Africa and Eastern Asia. However, when disaggregating the world regions into subregions based on river-basins with homogenous historical discharge trends, climate contributions to damages become statistically significant globally, in Asia and Latin America. In most regions, we find monotonous climate-induced damage trends but more years of observations would be needed to distinguish between the impacts of anthropogenic climate forcing and multidecadal oscillations.