Watershed discharge (WD) in the alpine regions, such as the upper reach of Yarlung Zangbo River Basin (YZRB), China, could have changed severely in response to climate changes. Yet, how hydrometeorological variables varied at different time scales and how WD varied in response to hydrometeorological variables in the alpine regions remained questions to be answered. The ensemble empirical mode decomposition (EEMD) method was employed in this study to investigate the nonlinear climate change trends (averaged and extreme states) and the associated multiscale impacts on WD variations over the upper reach of the YZRB during 1961–2009. All investigated hydroclimatic variables, i.e., precipitation, temperature, and WD, were found to be varied nonlinearly with clear multiscale oscillations characterizing great differences in the oscillation periods, corresponding significance levels, and variance contribution rates, among which precipitation posed a weak impact on WD variations, while temperature played a significant role in WD fluctuations. Furthermore, among all temperature extremes, the dominant index affecting WD variations was TXm (annual mean of the daily maximum temperature) but not TXx (annual maximum of the daily maximum temperature) at both interannual and interdecadal scales, which might be caused by that TXx increased evapotranspiration and reduced WD. A significant correlation between temperature (both averaged and partial extreme states) and annual WD at both interannual and interdecadal scales indicated that a synchronous change existed between them. The present study provided first insight into how hydrometeorological variables varied at different time scales and how WD fluctuated in response to hydrometeorological variables over the upper reach of the YZRB, China.