In this paper, we propose a new methodology for extracting river networks from satellite images. It combines morphological generalised geodesic transformations with hydrological overland flow simulations. The method requires the prior generation of a geodesic mask and a marker image by applying a series of transformations to the original image. These images are then combined so as to produce a pseudo digital elevation model whose valleys match the desired networks. The performance of the methodology is demonstrated for the extraction of river networks from a single band of a Landsat image. The method is generic in the sense that it can be extended for the extraction of other types of arborescent networks such as blood vessels in medical images.