Monitoring hydrological redistributions through their integrated gravitational effect is the primary aim of the Gravity Recovery and Climate Experiment (GRACE) mission. Time-variable gravity data from GRACE can be uniquely inverted to hydrology, since mass transfers located at or near the Earth's surface are much larger on shorter timescales than those taking place within the deeper Earth and because one can remove the contribution of atmospheric masses from air pressure data. Yet it has been proposed that at larger scales this may be achieved independently by measuring and inverting the elastic loading associated with redistributing masses, e.g., with the global network of the International GPS Service (IGS). This is particularly interesting as long as GRACE monthly gravity solutions do not (yet) match the targeted baseline accuracies at the lower spherical harmonic degrees. In this contribution (1) we describe and investigate an inversion technique which can deal jointly with GPS data and monthly GRACE solutions. (2) Previous studies with GPS data have used least squares estimators and impose solution constraints through low-degree spherical harmonic series truncation. Here we introduce a physically motivated regularization method that guarantees a stable inversion up to higher degrees, while seeking to avoid spatial aliasing. (3) We apply this technique to GPS data provided by the IGS service covering recent years. We can show that after removing the contribution ascribed to atmospheric pressure loading, estimated annual variations of continental-scale mass redistribution exhibit pattern similar to those observed with GRACE and predicted by a global hydrology model, although systematic differences appear to be present. (4) We compute what the relative contribution of GRACE and GPS would be in a joint inversion: Using current error estimates, GPS could contribute with up to 60% to degree 2 till 4 spherical harmonic coefficients and up to 30% for higher-degree coefficients.