Satellite imagery has been widely used to map global terrestrial river networks. However, existing methods and datasets still face the challenge of eliminating interference features and extracting continuous river networks. Terrestrial river networks profoundly shape the landscape but are also constrained by the landscape. Informed by this hydrogeomorphology knowledge, we propose a method to extract continuous river networks integrating 10 m resolution Sentinel-2 satellite imagery and the 1.0” resolution Copernicus digital elevation model (DEM). The remotely sensed modified normalized difference water index (MNDWI) is used to burn the DEM, representing the shaping function of rivers (water) on landscapes; height above the nearest drainage (HAND) topographic index is used to establish adaptively wide river areas of interest (AOIs), representing the constraint of landscapes on river morphology. Then, the remotely sensed water mask (RSWM) is extracted within AOIs by applying linear feature enhancements and adaptive thresholding. Subsequently, the RSWM and DEM-modeled drainage networks (DMDNs) are spatially overlaid to remove pseudo-river segments in the latter and connect river channel gaps in the former. Finally, isolated lakes are excluded because they do not intersect with the continuous river networks. We compare our mapping results with four 10 m resolution land use and land cover (LULC) datasets (FROM GLC10, ESA WorldCover, Esri Land Cover, and Dynamic World) across 16 diverse study sites globally, and investigate the ability of our method to extract multi-temporal river networks at two representative sites. The results show that, first, our method can accurately extract continuous river networks with highly sinuous channels, complex braided channels, and small rivers from heterogeneous image backgrounds, achieving Kappa coefficient of 0.840 ± 0.114, F1-score of 0.868 ± 0.111, overall accuracy of 0.961 ± 0.022, producer’s accuracy of 0.858 ± 0.171, and user’s accuracy of 0.901 ± 0.066, all of which are consistently higher and more stable compared with those of the four LULC datasets. Second, our mapping results more effectively preserve the connectivity of river networks (quantified by fewer yet longer connected components) than do the four comparison datasets. Third, our method can effectively identify water infilling of braided rivers, and seasonal expanding and shrinking of narrow upstream rivers. Finally, our method can distinguish continuous river networks from isolated lakes, thereby achieving a preliminary water type classification. In summary, our proposed method extends our knowledge of terrestrial river networks to 10 m spatial resolution and can be applied to higher-resolution river network mapping with the availability of higher-resolution satellite imagery and DEM products.