Cancers occur across species. Understanding what is consistent and varies across species can provide new insights into cancer initiation and evolution, with significant implications for animal welfare and wildlife conservation. We built the pan-species cancer digital pathology atlas (PANCAD) and conducted the first pan-species study of computational comparative pathology using a supervised convolutional neural network algorithm trained on human samples. The artificial intelligence algorithm achieves high accuracy in measuring immune response through single-cell classification for two transmissible cancers (canine transmissible venereal tumour, 0.94; Tasmanian devil facial tumour disease, 0.88). Furthermore, in 18 other vertebrate species (mammalia=11, reptilia=4, aves=2, and amphibia=1), accuracy (0.57-0.94) was influenced by cell morphological similarity preserved across different taxonomic groups, tumour sites, and variations in the immune compartment. A new metric, named morphospace overlap, was developed to guide veterinary pathologists towards rational deployment of this technology on new samples. This study provides the foundation and guidelines for transferring artificial intelligence technologies to veterinary pathology based on a new understanding of morphological conservation, which could vastly accelerate new developments in veterinary medicine and comparative oncology.