International nuclear safeguards inspectors do not have a method to verify the contents of sealed storage casks containing spent reactor fuel. The heavy shielding that is used to limit radiation emission attenuates and scatters photons and neutrons emitted by the fuel, and thereby hinders inspection with these probes. This problem is especially pressing given the policy decisions of several nations to begin permanent disposal of spent fuel in deep geological repositories. Radiography with cosmic-ray muons provides a potential solution, as muons are able to penetrate the cask and fuel and provide information on the cask contents. Here we show in simulation that muon scattering radiography can be used to inspect the contents of sealed geological storage casks, and can discern between a variety of plausible diversion scenarios. This technique can be applied immediately prior to permanent interment in a geological repository, giving inspectors a final opportunity to verify State declarations of spent fuel disposal.