Debris cover on glacier surfaces hampers the accurate detection of debris-covered ice using traditional techniques based on image band ratios. Therefore, this study tests a new automatic classification scheme for hierarchical mapping of glacier surfaces based on machine learning classifiers including k-nearest neighbors (KNN), support vector machine (SVM), gradient boosting (GB), decision tree (DT), random forest (RF) and multi-layer perceptron (MLP). Several raster layer combinations (synthetic aperture radar (SAR) coherence image derived from Sentinel-1 data, visible near-infrared to short wave infrared bands from Sentinel-2, thermal information from Landsat 8 and geomorphometric parameters from the Advanced Land Observing Satellite (ALOS) World 3D 30 m mesh (AW3D30) digital elevation model) were tested to delineate the debris-covered glaciers in the Gilgit-Baltistan, Pakistan and Shaksgam valley, China. The highest over classification accuracy (97%) was obtained using the RF classifier (followed by the GB and SVM with radial basis function kernel) and utilizing all of the multisensor Sentinel/Landsat/ALOS data. Notably, the RF classifier showed to be robust to parameter settings, fast and accurate for mapping debris-covered ice. GB classifier showed similar performance to RF, despite it having a moderately lower accuracy. Although SVM classifier was slower in the tuning of hyper-parameters, it still performed the third-best in terms of classification accuracy. As the multisensory data we used is freely and (near-)globally available, our methodology potentially could be applied for precise delineation of debris-covered glaciers in other areas.