The emergence of islands has been linked to spectacular radiations of diverse organisms. Although penguins spend much of their lives at sea, they rely on land for nesting, and a high proportion of extant species are endemic to geologically young islands. Islands may thus have been crucial to the evolutionary diversification of penguins. We test this hypothesis using a fossil-calibrated phylogeny of mitochondrial genomes (mitogenomes) from all extant and recently extinct penguin taxa. Our temporal analysis demonstrates that numerous recent island-endemic penguin taxa diverged following the formation of their islands during the Plio-Pleistocene, including the Galápagos (Galápagos Islands), northern rockhopper (Gough Island), erect-crested (Antipodes Islands), Snares crested (Snares) and royal (Macquarie Island) penguins. Our analysis also reveals two new recently extinct island-endemic penguin taxa from New Zealand's Chatham Islands: Eudyptes warhami sp. nov. and a dwarf subspecies of the yellow-eyed penguin, Megadyptes antipodes richdalei ssp. nov. Eudyptes warhami diverged from the Antipodes Islands erect-crested penguin between 1.1 and 2.5 Ma, shortly after the emergence of the Chatham Islands (∼3 Ma). This new finding of recently evolved taxa on this young archipelago provides further evidence that the radiation of penguins over the last 5 Ma has been linked to island emergence. Mitogenomic analyses of all penguin species, and the discovery of two new extinct penguin taxa, highlight the importance of island formation in the diversification of penguins, as well as the extent to which anthropogenic extinctions have affected island-endemic taxa across the Southern Hemisphere's isolated archipelagos.