Vast quantities of debris are beaching at remote islands in the western Indian Ocean. We carry out marine dispersal simulations incorporating currents, waves, winds, beaching, and sinking, for both terrestrial and marine sources of debris, to predict where this debris comes from. Our results show that most terrestrial debris beaching at these remote western Indian Ocean islands drifts from Indonesia, India, and Sri Lanka. Debris associated with fisheries and shipping also poses a major risk. Debris accumulation at Seychelles is likely seasonal, peaking during February-April. This pattern is driven by monsoonal winds and may be amplified during positive Indian Ocean Dipole and El-Niño events. Our results underline the vulnerability of small island states to marine plastic pollution, and are a crucial step towards improved management of the issue. The trajectories used in this study are available for download, and our analyses can be rerun under different parameter choices.