Changes in carbon storage in terrestrial ecosystems are a consequence of shifts in the balance between net primary production (NPP) and heterotrophic respiration (RH). Historical climatic variations which favored NPP over RH may have led to increased ecosystem carbon storage and might account for at least part of the “missing” sink required to balance the current century's global carbon budget. To test this hypothesis, we employed a georeferenced global terrestrial biosphere model of 0.5° spatial resolution. The model was driven from an assumed equilibrium in 1900 using gridded historical time series of monthly temperature and precipitation and the historical record of changes in atmospheric CO2 concentration. Interannual variability in climate induced interannual changes in terrestrial biospheric carbon storage and net carbon exchange with the atmosphere of the order of 1–2 Gt C yr−1. With climate change alone, global biospheric carbon storage declined by 1% (23 Gt C) over the period 1900–1988. With the addition of a moderate CO2 fertilization response, biospheric carbon storage increased by 3% (57 Gt C), primarily as a consequence of changes in NPP and litter inputs to the soil system. With CO2 fertilization, the model's cumulative carbon sink for the period 1900–1988 accounts for about 69% of the missing sink derived by deconvolution. For the period 1950–1988, the modeled sink is about 56% of the missing sink. Our results suggest that the temporal evolution of the missing sink over the period 1900–1988 could be a response of the terrestrial biosphere to changes in climate and atmospheric CO2 or perhaps climate change alone. The discrepancy in the magnitudes of the modeled and deconvolved sinks may be due to limitations of the biospheric model or to overestimates of the land‐use source flux.