Evolution of vertebrate endemics in oceanic islands follows a predictable pattern, known as the island rule, according to which gigantism arises in originally small-sized species and dwarfism in large ones. Species of extinct insular giant rodents are known from all over the world. In the Canary Islands, two examples of giant rats, †Canariomys bravoi and †Canariomys tamarani, endemic to Tenerife and Gran Canaria, respectively, disappeared soon after human settlement. The highly derived morphological features of these insular endemic rodents hamper the reconstruction of their evolutionary histories. We have retrieved partial nuclear and mitochondrial data from †C. bravoi and used this information to explore its evolutionary affinities. The resulting dated phylogeny confidently places †C. bravoi within the African grass rat clade (Arvicanthis niloticus). The estimated divergence time, 650 000 years ago (95% higher posterior densities: 373 000–944 000), points toward an island colonization during the Günz–Mindel interglacial stage. †Canariomys bravoi ancestors would have reached the island via passive rafting and then underwent a yearly increase of mean body mass calculated between 0.0015 g and 0.0023 g; this corresponds to fast evolutionary rates (in darwins (d), ranging from 7.09 d to 2.78 d) that are well above those observed for non-insular mammals.