Terrestrial biophysical variables play an essential role in quantifying the amount of energy budget, water cycle, and carbon sink over the Three-River Headwaters Region of China (TRHR). However, direct field observations are missing in this region, and few studies have focused on the long-term spatiotemporal variations of terrestrial biophysical variables. In this study, we evaluated the spatiotemporal dynamics of biophysical variables including meteorological variables, vegetation, and evapotranspiration (ET) over the TRHR, and analyzed the response of vegetation and ET to climate change in the period from 1982 to 2015. The main input gridded datasets included meteorological reanalysis data, a satellite-based vegetation index dataset, and the ET product developed by a process-based Priestley–Taylor algorithm. Our results illustrate that: (1) The air temperature and precipitation over the TRHR increased by 0.597 °C and 41.1 mm per decade, respectively, while the relative humidity and surface downward shortwave radiation declined at a rate of 0.9% and 1.8 W/m2 per decade during the period 1982–2015, respectively. We also found that a ‘dryer warming’ tendency and a ‘wetter warming’ tendency existed in different areas of the TRHR. (2) Due to the predominant ‘wetter warming’ tendency characterized by the increasing temperature and precipitation, more than 56.8% of areas in the TRHR presented a significant increment in vegetation (0.0051/decade, p < 0.05), particularly in the northern and western meadow areas. When energy was the limiting factor for vegetation growth, temperature was a considerably more important driving factor than precipitation. (3) The annual ET of the TRHR increased by 3.34 mm/decade (p < 0.05) with an annual mean of 230.23 mm/year. More importantly, our analysis noted that ET was governed by terrestrial water supply, e.g., soil moisture and precipitation in the arid region of the western TRHR. By contrast, atmospheric evaporative demand derived by temperature and relative humidity was the primary controlling factor over the humid region of the southeastern TRHR. It was noted that land management activities, e.g., irrigation, also had a nonnegligible impact on the temporal and spatial variation of ET.