Invertebrates dominate many terrestrial ecosystems in terms of biomass, and they also structure ecosystems through their roles as pollinators, detritivores, primary consumers, predators and prey. Invasive rodents (rats and mice) are known to have detrimental effects on many island invertebrates, although these effects are seldom quantified or ecologically understood. Here we provide evidence of the effects of invasive rats (Rattus spp.) on island invertebrate populations using a large-scale natural experiment. We investigated the effects of invasive rats on Falkland camel crickets (Parudenus spp.) in the Falkland Islands (South Atlantic) by comparing an index of camel cricket relative abundance between 18 rat-infested islands, six rat-eradicated islands and 13 naturally rat-free islands (in total, 37 islands). Our study provided two key results. First, camel crickets were up to an order of magnitude more abundant on rat-free islands than on rat-infested or rat-eradicated islands. This difference was larger in native tussac grass Poa flabellata than in other vegetation types. Second, camel cricket populations recovered after rat eradication, because the relative abundance of camel crickets on rat-eradicated islands was intermediate between those of naturally rat-free and rat-infested islands, and among rat-eradicated islands relative abundance was lowest where rats had been cleared most recently. Our results demonstrate severe suppression of a superabundant and large-bodied island endemic invertebrate by invasive rodents, and its prompt recovery after rodent eradication.