The use of cover crops (CCs) is a promising cropland management practice with multiple benefits, notably in reducing soil erosion and increasing soil organic carbon (SOC) storage. However, the current ability to represent these factors in land surface models remains limited to small scales or simplified and lumped approaches due to the lack of a sediment-carbon erosion displacement scheme. This precludes a thorough understanding of the consequences of introducing a CC into agricultural systems. In this work, this problem was addressed in two steps with the spatially distributed CE-DYNAM model. First, the historical effect of soil erosion, transport, and deposition on the soil carbon budget at a continental scale in Europe was characterized since the early industrial era, using reconstructed climate and land use forcings. Then, the impact of two distinct policy-oriented scenarios for the introduction of CCs were evaluated, covering the European cropping systems where surface erosion rates or nitrate susceptibility are critical. The evaluation focused on the increase in SOC storage and the export of particulate organic carbon (POC) to the oceans, compiling a continental-scale carbon budget. The results indicated that Europe exported 1.95 TgC/year of POC to the oceans in the last decade, and that CCs can contribute to reducing this amount while increasing SOC storage. Compared to the simulation without CCs, the additional rate of SOC storage induced by CCs peaked after 10 years of their adoption, followed by a decrease, and the cumulative POC export reduction stabilized after around 13 years. The findings indicate that the impacts of CCs on SOC and reduced POC export are persistent regardless of their spatial allocation adopted in the scenarios. Together, the results highlight the importance of taking the temporal aspect of CC adoption into account and indicate that CCs alone are not sufficient to meet the targets of the 4‰ initiative. Despite some known model limitations, which include the lack of feedback of erosion on the net primary productivity and the representation of carbon fluxes with an emulator, the current work constitutes the first approach to successfully couple a distributed routing scheme of eroded carbon to a land carbon model emulator at a reasonably high resolution and continental scale.