Invasive alien species are a major threat to native insular species. Eradicating invasive mammals from islands is a feasible and proven approach to prevent biodiversity loss. We developed a conceptual framework to identify globally important islands for invasive mammal eradications to prevent imminent extinctions of highly threatened species using biogeographic and technical factors, plus a novel approach to consider socio-political feasibility. We applied this framework using a comprehensive dataset describing the distribution of 1,184 highly threatened native vertebrate species (i.e. those listed as Critically Endangered or Endangered on the IUCN Red List) and 184 non-native mammals on 1,279 islands worldwide. Based on extinction risk, irreplaceability, severity of impact from invasive species, and technical feasibility of eradication, we identified and ranked 292 of the most important islands where eradicating invasive mammals would benefit highly threatened vertebrates. When socio-political feasibility was considered, we identified 169 of these islands where eradication planning or operation could be initiated by 2020 or 2030 and would improve the survival prospects of 9.4% of the Earth's most highly threatened terrestrial insular vertebrates (111 of 1,184 species). Of these, 107 islands were in 34 countries and territories and could have eradication projects initiated by 2020. Concentrating efforts to eradicate invasive mammals on these 107 islands would benefit 151 populations of 80 highly threatened vertebrates and make a major contribution towards achieving global conservation targets adopted by the world's nations.