This study proposes an original method for tree species classification by satellite remote sensing. The method uses multitemporal multispectral (Landsat OLI) and hyperspectral (Resurs-P) data acquired from determined vegetation periods. The method is based on an original database of spectral features taking into account seasonal variations of tree species spectra. Changes in the spectral signatures of forest classes are analyzed and new spectral–temporal features are created for the classification. Study sites are located in the Czech Republic and northwest (NW) Russia. The differences in spectral reflectance between tree species are shown as statistically significant in the sub-seasons of spring, first half of summer, and main autumn for both study sites. Most of the errors are related to the classification of deciduous species and misclassification of birch as pine (NW Russia site), pine as mixture of pine and spruce, and pine as mixture of spruce and beech (Czech site). Forest species are mapped with accuracy as high as 80% (NW Russia site) and 81% (Czech site). The classification using multitemporal multispectral data has a kappa coefficient 1.7 times higher than does that of classification using a single multispectral image and 1.3 times greater than that of the classification using single hyperspectral images. Potentially, classification accuracy can be improved by the method when applying multitemporal satellite hyperspectral data, such as in using new, near-future products EnMap and/or HyspIRI with high revisit time.