The Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission, by providing a precise estimate of the marine geoid height, will allow the determination of absolute geostrophic velocities at the surface of the ocean with unprecedented accuracy. The resulting impact on oceanic flux estimates is quantified within a climatological inverse model of the Atlantic in terms of reduction of uncertainties in volume transports. These uncertainty reductions are obtained by replacing the error spectrum of present-day geoid models by the error spectrum expected for the GOCE mission. The impact is large in the Circumpolar Current, with relative uncertainty reductions reaching 50% in the upper layers of the ocean, and 40% in the whole water column. It is also large in regions of sharp oceanic fronts like the Gulf Stream or the Brazil Current, with uncertainty reductions reaching 60% in the upper layers of the ocean. The reduction in transport uncertainties is large enough in absolute terms to have a significant impact on estimates of important climate processes like the rate of overturning in the Atlantic or the exchange of water between the Circumpolar Current and the South Atlantic. The impact of the Gravity Recovery and Climate Experiment (GRACE) mission, estimated within the same inverse model, is on average less than half the impact of GOCE because of the lower precision of this mission at small spatial scales. The fact that uncertainties in the baroclinic component of the velocity field limit the impact of GOCE at depths points to the need for precise in situ observations to complement gravity and altimetric observations.