Ocean CO2 uptake, moderated by the slow mixing of dissolved inorganic carbon to the ocean depths, is estimated to have a duration of ~1,000 years when the atmosphere is held at a constant stabilized CO2 concentration. This timescale is found to be several times longer than the relaxation time for the atmosphere-ocean system to come to equilibrium when forced by a CO2 emission impulse. Furthermore, the 1,000 year timescale is found to be insensitive to atmospheric CO2 concentration level. Beyond 2,000 years, sediment CaCO3 neutralization becomes the dominant mechanism for CO2 uptake further extending the timescale of the ocean carbon sink. The equilibration time of the atmosphere-ocean system, on the other hand, is shown to lengthen with increasing magnitude of CO2 emissions. Estimates are based on the response of a 3D-ocean carbon cycle model, and this behavior explained using the analytic solution of a simple box model.