The ever-increasing use of mouse models in preclinical neuroscience research calls for an improvement in the methods used to translate findings between mouse and human brains. Previously, we showed that the brains of primates can be compared in a direct quantitative manner using a common reference space built from white matter tractography data (Mars et al., 2018b). Here, we extend the common space approach to evaluate the similarity of mouse and human brain regions using openly accessible brain-wide transcriptomic data sets. We show that mouse-human homologous genes capture broad patterns of neuroanatomical organization, but the resolution of cross-species correspondences can be improved using a novel supervised machine learning approach. Using this method, we demonstrate that sensorimotor subdivisions of the neocortex exhibit greater similarity between species, compared with supramodal subdivisions, and mouse isocortical regions separate into sensorimotor and supramodal clusters based on their similarity to human cortical regions. We also find that mouse and human striatal regions are strongly conserved, with the mouse caudoputamen exhibiting an equal degree of similarity to both the human caudate and putamen.