Using a uniform velocity/density scaling, we have inverted the seismically inferred 3‐dimensional structure of the whole mantle for the radial viscosity structure which best fits the geoid. We are able to obtain 60–72% variance reductions for three different S‐wave tomographic models. The resulting viscosity structures are remarkably similar, showing a high viscosity lid, a low viscosity zone in the transition region and a high viscosity lower mantle. A resolution analysis indicates that the viscosity structure in the upper mantle is well resolved by the data, however the resolution in the lower mantle is poorer. Our models are in general agreement with previous studies except that our inversions prefer a low viscosity layer at 400–670 km as opposed to 100–400 km.