Abstract Mesoscale eddies are a dominant reservoir of kinetic energy in the ocean and play an important role in the transport and stirring of tracers such as heat and carbon. These effects need to be parameterized in most ocean models. A number of studies have observationally quantified eddy effects, but most of these have focused on the diffusivity of passive tracers (Solomon‐Redi diffusivity). However, passive tracer diffusivity is not directly informative about the quasi‐Stokes transport, since this requires estimates of the buoyancy diffusivity (also known as the Gent‐McWilliams diffusivity). Here we obtain the first global observational estimates of the quasi‐Stokes transport, assuming that mesoscale eddies diffuse potential vorticity (PV) rather than buoyancy. These are also used to estimate the corresponding buoyancy diffusivity, which is what is needed in coarse‐resolution ocean models employing the Gent‐McWilliams parameterization. These observational estimates may be used as constraints for future development and tuning of mesoscale parameterizations.