Strong seasonal variations of horizontal and vertical positions are observed on GPS time series from stations located in Nepal, India, and Tibet (China). We show that this geodetic deformation can be explained by seasonal variations of continental water storage driven by the monsoon. For this purpose, we use satellite data from the Gravity Recovery and Climate Experiment to determine the time evolution of surface loading. We compute the expected geodetic deformation assuming a perfectly elastic Earth model. We consider Green's functions, describing the surface deformation response to a point load, for an elastic homogeneous half-space model and for a layered nonrotating spherical Earth model based on the Preliminary Reference Earth Model and a local seismic velocity model. The amplitude and phase of the seasonal variation of the vertical and horizontal geodetic positions can be jointly adjusted only with the layered Earth model, while an elastic half-space model fails, emphasizing the importance of using a realistic Earth elastic structure to model surface displacements induced by surface loading. We demonstrate, based on a formal inversion, that the fit to the geodetic data can be improved by adjusting the layered Earth model. Therefore, the study also shows that the modeling of geodetic seasonal variations provides a way to probe the elastic structure of the Earth, even in the absence of direct measurements of surface load variations