We have extended the GENIE‐1 Earth system model to include a representation of sedimentary stratigraphy and the preservation of biogenic carbonates delivered to the ocean floor. This has enabled us to take a novel approach in diagnosing modern marine carbon cycling: assimilating observation of the calcium carbonate (CaCO3) content of deep‐sea sediments with an ensemble Kalman filter. The resulting calibrated model predicts a mean surface sediment content (32.5 wt%) close to the observed value (34.8 wt%), and a global burial rate of CaCO3 in deep sea sediments of 0.121 PgC yr−1, in line with recent budget estimates of 0.10−0.14 PgC yr−1. We employ the GENIE‐1 model in quantifying the multimillennial‐scale fate of fossil fuel CO2 emitted to the atmosphere. In the absence of any interaction between ocean and sediments, an equilibrium partitioning of CO2 is reached within ∼1000 years of emissions ceasing, with 34% (645 ppm) remaining in the atmosphere out of a total fossil fuel burn of 4173 PgC. An additional 12% of CO2 emissions (223 ppm) are sequestered as bicarbonate ions (HCO3−) by reaction with deep‐sea carbonates (“seafloor CaCO3 neutralization”) on a timescale of ∼1.7 ka. Excess of carbonate weathering on land over deep‐sea burial results in a further net transformation of 14% of CO2 emissions (261 ppm) into HCO3− (“terrestrial CaCO3 neutralization”) on a timescale of ∼8.3 ka. We have also assessed the importance of a changing climate in modulating the stabilization of atmospheric CO2 through ocean‐sediment interaction. Increased ocean stratification suppresses particulate organic carbon export, which in turn enhances seafloor CaCO3 preservation. The resulting reduction in the sequestration of fossil fuel CO2 represents a new positive feedback on millennial‐scale climate change.