A novel method to estimate annual mean heat, water, and gas exchange fluxes between the ocean and the atmosphere is proposed that is complementary to the traditional approach based on air-sea gradients and bulk exchange parameterization. The new approach exploits the information on surface exchange fluxes contained in the distribution of temperature, salinity, and dissolved gases in the ocean interior. We use an Ocean General Circulation Model to determine how the distribution in the ocean interior is linked to surface fluxes. We then determine with least squares the surface fluxes that are most compatible with the observations. To establish and test the method, we apply it to ocean temperature data to estimate heat fluxes across the air-sea interface for which a number of climatological estimates exists. We also test the sensitivity of the inversion results to data coverage, differences in ocean transport, variations in the surface flux pattern and a range of spatial resolutions. We find, on the basis of the World Ocean Circulation Experiment (WOCE) data network augmented with selected high-quality pre-WOCE data, that we are able to constrain heat exchange fluxes for 10--15 regions of the ocean, whereby these fluxes nearly balance globally without enforcing a conservation constraint. Our results agree well with heat flux estimates on the basis of bulk exchange parameterization, which generally require constraints to ensure a global net heat flux of zero. We also find that the heat transports implied by our inversely estimated fluxes are in good agreement with a large range of heat transport estimates based on hydrographic data. Increasing the number of regions beyond the 10--15 regions considered here is severely limited because of modeling errors. The inverse method is fairly robust to the modeling of the spatial patterns of the surface fluxes; however, it is quite sensitive to the modeling of ocean transport. The most striking difference between our estimates and the heat flux climatologies is a large heat loss of 0.64 PW to the atmosphere from the Southern Ocean and a large heat gain by the subpolar South Atlantic of 0.56 PW. These results are consistent with the large gain of carbon dioxide called for by Takahashi et al. [1999] in his recent analysis of the air-sea flux of carbon dioxide but inconsistent with the large loss of oxygen and carbon dioxide such as those of Stephens et al. [1998]. ¿ 2001 American Geophysical Union