Seasonal hydrological surveys and long-term current measurements carried out during a wide investigation of the central Mediterranean, connecting the eastern and western parts of the basin with the Tyrrhenian Sea, are used to estimate the absolute geostrophic flow through the region applying an inverse methodology. The inverse box model prescribes conservation of water properties (mass, heat, and salt) inside closed boxes of water, as well as the imposition of mean fluxes by direct current measurements. The model result is a mean circulation of the region during four different periods, along with simultaneous evaluation of water fluxes through the three boundary sections and the associated uncertainties. The overall situation, besides confirming previous qualitative knowledge on the mean circulation at all levels, provides a novel quantitative pattern of the water mass exchange in a region that is crucial for the assessment of a more realistic budget for the whole basin. The positive results obtained indicate that the inverse method may be considered an effective powerful tool for successful applications at regional scale.