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 build a pan-species cancer digital pathology atlas (panspecies.ai) and conduct a 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). In 18 other vertebrate species (mammalia = 11, reptilia = 4, aves = 2, and amphibia = 1), accuracy (range 0.57-0.94) is influenced by cell morphological similarity preserved across different taxonomic groups, tumour sites, and variations in the immune compartment. Furthermore, a spatial immune score based on artificial intelligence and spatial statistics is associated with prognosis in canine melanoma and prostate tumours. A metric, named morphospace overlap, is 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 understanding of morphological conservation, which could vastly accelerate developments in veterinary medicine and comparative oncology.