With the development of satellite altimetry, it is possible to infer the geostrophic velocity of the surface ocean currents, if the geoid and the position of the satellite are known accurately. Errors in current geoid models and orbit computations, both due primarily to errors in the Earth's gravity field model, have limited the use of altimeter data for this purpose. The objective of this investigation is to demonstrate that altimeter data can be used in a joint solution to simultaneously estimate the quasi‐stationary sea surface topography, ζ, and the model for the gravity field. Satellite tracking data from twelve satellites were used along with Seasat altimeter data for the solution. The estimated model of ζ compares well at long wavelengths with the hydrographic model of ζ. Covariance analysis indicates that the geoid is separable from ζ up to degree 9, at which point geoid error is comparable to the signal of ζ.