The Three-River Source Region (TRSR) of the Tibetan Plateau (TP) is regarded as the “Chinese water tower”. Climate warming and the associated degradation of permafrost might change the water cycle and affect the alpine vegetation growth in the TRSR. However, the quantitative changes in the water budget and their impacts on the vegetation in the TRSR are poorly understood. In this study, the spatial-temporal changes in the hydrological variables and the normalized difference vegetation index (NDVI) during 2003–2014 were investigated using multiple satellite data and a remote sensing energy balance model. The results indicated that precipitation showed an increasing trend at a rate of 14.0 mm 10 a−1, and evapotranspiration (ET) showed a slight decreasing trend. The GRACE-derived total water storage (TWS) change presented a significant increasing trend at a rate of 35.1 mm a−1. The change in groundwater (GW) which showed an increasing trend at a rate of 18.5 mm a−1, was estimated by water budget. The time lag of the GRACE-TWS that was influenced by precipitation was more obviously than was the GLDAS-SM (Soil Moisture) change. The vegetation in the TRSR was greening during the study period, and the accumulation of the NDVI increased rapidly after 2008. The effect of total TWS and GLDAS-SM on vegetation was considerably more than that the effects of other factors in this region. It was concluded that the hydrological cycle had obviously changed and that more soil water was transferred into the GW since the aquiclude changed due to climate warming. The increasing area and number of lakes and the thickening of the active layer in the permafrost area led to the greater infiltration of surface water into the groundwater, which resulted in increased water storage.