Climate change poses potential challenges to sensitive areas, such as high-elevation regions. The Yarlung Zangbo River (YLZR) basin is located in the southeast of the Qinghai-Tibetan Plateau. It contains large amounts of snow and numerous glaciers that are vulnerable to climate change. Based on daily observational data at 17 meteorological stations in and around the YLZR basin during 1957–2015, the variability of precipitation, air temperature, and streamflow were analyzed. The nonparametric Mann–Kendall test, Sen’s slope estimate method, cross wavelet transform (XWT), and wavelet coherence (WTC) were used to identify the annual seasonal trends. the abrupt changes of precipitation and air temperature, and their associations with large-scale circulation. The results showed that the YLZR basin experienced an overall rapid warming and wetting during the study period, with an average warming rate of 0.33 °C/10 a and wetting rate of 4.25 mm/10a, respectively. Abrupt change points in precipitation and air temperature occurred around the 1970s and 1990s, respectively. The abrupt change points of three hydrological stations occurred around the late 1960s and the late 1990s, respectively. The precipitation, annual average temperature, and the streamflow of the three hydrological stations were negatively correlated with the Pacific decadal oscillation (PDO) and the multivariate El Niño-Southern Oscillation (ENSO) index (MEI), reaching a significant level of 0.05.