Impacts of low-latitude, explosive volcanic eruptions on climate and the carbon cycle are quantified by forcing a comprehensive, fully coupled carbon cycle-climate model with pulse-like stratospheric aerosol optical depth changes. The model represents the radiative and dynamical response of the climate system to volcanic eruptions and simulates a decrease of global and regional atmospheric surface temperature, regionally distinct changes in precipitation, a positive phase of the North Atlantic Oscillation, and a decrease in atmospheric CO₂ after volcanic eruptions. The volcanic-induced cooling reduces overturning rates in tropical soils, which dominates over reduced litter input due to soil moisture decrease, resulting in higher land carbon inventories for several decades. The perturbation in the ocean carbon inventory changes sign from an initial weak carbon sink to a carbon source. Positive carbon and negative temperature anomalies in subsurface waters last up to several decades. The multi-decadal decrease in atmospheric CO₂ yields a small additional radiative forcing that amplifies the cooling and perturbs the Earth System on longer time scales than the atmospheric residence time of volcanic aerosols. In addition, century-scale global warming simulations with and without volcanic eruptions over the historical period show that the ocean integrates volcanic radiative cooling and responds for different physical and biogeochemical parameters such as steric sea level or dissolved oxygen. Results from a suite of sensitivity simulations with different magnitudes of stratospheric aerosol optical depth changes and from global warming simulations show that the carbon cycle-climate sensitivity γ, expressed as change in atmospheric CO₂ per unit change in global mean surface temperature, depends on the magnitude and temporal evolution of the perturbation, and time scale of interest. On decadal time scales, modeled γ is several times larger for a Pinatubo-like eruption than for the industrial period and for a high emission, 21st century scenario.