The Ordovician-Silurian transition (∼ 455-430 Ma) is characterized by repeated climatic perturbations, concomitant with major changes in the global oceanic redox state best exemplified by the periodic deposition of black shales. The relationship between the climatic evolution and the oceanic redox cycles, however, remains largely debated. Here, using an ocean-atmosphere general circulation model accounting for ocean biogeochemistry (MITgcm), we investigate the mechanisms responsible for the burial of organic carbon immediately before, during and right after the latest Ordovician Hirnantian (445-444 Ma) glacial peak. Our results are compared with recent sedimentological and geochemical data. We show that the late Katian time slice (∼ 445 Ma), typified by the deposition of black shales at tropical latitudes, represents an unperturbed oceanic state, with regional organic carbon burial driven by the surface primary productivity. During the Hirnantian, our experiments predict a global oxygenation event, in agreement with the disappearance of the black shales in the sedimentary record. This suggests that deep-water burial of organic matter may not be a tenable triggering factor for the positive carbon excursion reported at that time. Our simulations indicate that the perturbation of the ocean circulation induced by the release of freshwater, in the context of the post-Hirnantian deglaciation, does not sustain over sufficiently long geological periods to cause the Rhuddanian (∼ 444 Ma) oceanic anoxic event. Input of nutrients to the ocean, through increased continental weathering and the leaching of newly-exposed glaciogenic sediments, may instead constitute the dominant control on the spread of anoxia in the early Silurian.