Brain and breast tumors cause significant morbidity and mortality worldwide. Accurate and expedient histological diagnosis of patients' tumor specimens is required for subsequent treatment and prognostication. Currently, histology slides are visually inspected by trained pathologists, but this process is both time and labor-intensive. In this paper, we propose an automated process to classify histology slides of both brain and breast tissues using the Google Inception V3 convolutional neural network (CNN). We report successful automated classification of brain histology specimens into normal, low grade glioma (LGG) or high grade glioma (HGG). We also report for the first time the benefit of transfer learning across different tissue types. Pre-training on a brain tumor classification task improved CNN performance accuracy in a separate breast tumor classification task, with the F1 score improving from 0.547 to 0.913. We constructed a dataset using brain histology images from our own hospital and a public breast histology image dataset. Our proposed method can assist human pathologists in the triage and inspection of histology slides to expedite medical care. It can also improve CNN performance in cases where the training data is limited, for example in rare tumors, by applying the learned model weights from a more common tissue type.