The ocean has absorbed the equivalent of 39% of industrial-age fossil carbon emissions, significantly modulating the growth rate of atmospheric CO2 and its associated impacts on climate. Despite the importance of the ocean carbon sink to climate, our understanding of the causes of its interannual-to-decadal variability remains limited. This hinders our ability to attribute its past behavior and project its future. A key period of interest is the 1990s, when the ocean carbon sink did not grow as expected. Previous explanations of this behavior have focused on variability internal to the ocean or associated with coupled atmosphere/ocean modes. Here, we use an idealized upper ocean box model to illustrate that two external forcings are sufficient to explain the pattern and magnitude of sink variability since the mid-1980s. First, the global-scale reduction in the decadal-average ocean carbon sink in the 1990s is attributable to the slowed growth rate of atmospheric pCO2. The acceleration of atmospheric pCO2 growth after 2001 drove recovery of the sink. Second, the global sea surface temperature response to the 1991 eruption of Mt Pinatubo explains the timing of the global sink within the 1990s. These results are consistent with previous experiments using ocean hindcast models with and without forcing from variable atmospheric pCO2 and climate variability. The fact that variability in the growth rate of atmospheric pCO2 directly imprints on the ocean sink implies that there will be an immediate reduction in ocean carbon uptake as atmospheric pCO2 responds to cuts in anthropogenic emissions.