The Arctic is warming far faster than the global average, threatening the release of large amounts of carbon presently stored in frozen permafrost soils. Increasing Earth’s albedo by the injection of sulfate aerosols into the stratosphere has been proposed as a way of offsetting some of the adverse effects of climate change. We examine this hypothesis in respect of permafrost carbon-climate feedbacks using the PInc-PanTher process model driven by seven earth system models running the Geoengineering Model Intercomparison Project (GeoMIP) G4 stratospheric aerosol injection scheme to reduce radiative forcing under the Representative Concentration Pathway (RCP) 4.5 scenario. Permafrost carbon released as CO2 is halved and as CH4 by 40% under G4 compared with RCP4.5. Economic losses avoided solely by the roughly 14 Pg carbon kept in permafrost soils amount to about US$ 8.4 trillion by 2070 compared with RCP4.5, and indigenous habits and lifestyles would be better conserved.