An analysis of ocean volume, heat, and freshwater transports from a fully constrained general circulation model (GCM) is described. Output from a data synthesis, or state estimation, method is used by which the model was forced to large-scale, time-varying global ocean data sets over 1993 through 2000. Time-mean horizontal transports, estimated from this fully time-dependent circulation, have converged with independent time-independent estimates from box inversions over most parts of the world ocean but especially in the southern hemisphere. However, heat transport estimates differ substantially in the North Atlantic where our estimates result in only 1/2 previous results. The models drift over the estimation period is consistent with observations from TOPEX/Poseidon in their spatial pattern, but smaller in their amplitudes by about a factor of 2. Associated temperature and salinity changes are complex, and both point toward air–sea interaction over water mass formation regions as the primary source for changes in the deep ocean. The estimated mean circulation around Australia involves a net volume transport of 11 Sv through the Indonesian Throughflow and the Mozambique Channel. In addition, we show that this flow regime exists on all timescales above 1 month, rendering the variability in the South Pacific strongly coupled to the Indian Ocean. Moreover, the dynamically consistent variations in the model show temporal variability of oceanic heat transports, heat storage, and atmospheric exchanges that are complex and with a strong dependence upon location, depth, and timescale. Our results demonstrate the great potential of an ocean state estimation system to provide a dynamical description of the time-dependent observed heat transport and heat content changes and their relation to air–sea interactions.