Morphology-based classification of cells in the bone marrow aspirate (BMA) is a key step in the diagnosis and management of hematologic malignancies. However, it is time-intensive and must be performed by expert hematopathologists and laboratory professionals. We curated a large, high-quality dataset of 41,595 hematopathologist consensus-annotated single-cell images extracted from BMA whole slide images (WSIs) containing 23 morphologic classes from the clinical archives of the University of California, San Francisco. We trained a convolutional neural network, DeepHeme, to classify images in this dataset, achieving a mean area under the curve (AUC) of 0.99. DeepHeme was then externally validated on WSIs from Memorial Sloan Kettering Cancer Center, with a similar AUC of 0.98, demonstrating robust generalization. When compared to individual hematopathologists from three different top academic medical centers, the algorithm outperformed all three. Finally, DeepHeme reliably identified cell states such as mitosis, paving the way for image-based quantification of mitotic index in a cell-specific manner, which may have important clinical applications.