Satellite precipitation products have been largely improved in the recent years particularly with the launch of the global precipitation measurement (GPM) core satellite. Moreover, the development of techniques for exploiting the information provided by satellite soil moisture to complement/enhance precipitation products have improved the accuracy of accumulated rainfall estimates over land. Such satellite enhanced precipitation products, available with a short latency (< 1 day), represent an important and new source of information for river flow prediction and water resources management, particularly in developing countries in which ground observations are scarcely available and the access to such data is not always ensured. In this study, three recently developed rainfall products obtained from the integration of GPM rainfall and satellite soil moisture products have been used; namely GPM+SM2RAIN, PRISM-SMOS, and PRISM-SMAP. The prediction of observed daily river discharge at 10 basins located in Europe (4), West Africa (3) and South Africa (3) is carried out. For comparison, we have also considered three rainfall products based on: (1) GPM only, i.e., the Early Run version of the Integrated Multi-Satellite Retrievals for GPM (GPM-ER), (2) rain gauges, i.e., the Global Precipitation Climatology Centre, and (3) the latest European Centre for Medium-Range Weather Forecasts reanalysis, ERA5. Three different conceptual and lumped rainfall-runoff models are employed to obtain robust and reliable results over the 3-year data period 2015-2017. Results indicate that, particularly over scarcely gauged areas (West Africa), the integrated products outperform both ground- and reanalysis-based rainfall estimates. For all basins, the GPM+SM2RAIN product is performing the best among the short latency products with mean Kling-Gupta Efficiency (KGE) equal to 0.87, and significantly better than GPM-ER (mean KGE = 0.77). The integrated products are found to reproduce particularly well the high flows. These results highlight the strong need to disseminate such integrated satellite rainfall products for hydrological (and agricultural) applications in poorly gauged areas such as Africa and South America.