With a warming climate, solar activity including Sunspot Number (SSN) and large-scale climate phenomena including EI Niño-Southern Oscillation (ENSO), Pacific Decadal Oscillation (PDO) and Arctic Oscillation (AO) have induced changes in climate extremes and changes in the hydrological cycle in arid-semiarid regions of the world, thus a detailed investigation of climate variability can play a key role in water resources management, drought monitoring, ecological restoration and sustainable development. In this study, we used wavelet coherence (WTC) based on continuous wavelet transform (CWT) to assess the impacts of SSN, ENSO, PDO and AO on multiple interacting hydrological processes and identify the teleconnection patterns and lead-lag relationships between the four principal modes and changes in extreme temperature and precipitation events, meteorological drought, and streamflow variability in Xinjiang, an arid-semiarid region of China. The results indicated that solar activity and climatic oscillations were viewed as the primary drivers for periodic variation of extreme temperature events and the evolution of drought in Xinjiang. For instance, the ENSO positively affected warm extremes with intermittent coherence in the 2–6-year band during 1984–2000 and had negative correlations with cold extremes in the 2–6-year band at the interannual scale. Compared with warm extremes, variability in cold extremes was much more sensitive to the activity pattern of AO. It was clear that the coherence of temperature variables in Xinjiang with PDO was weaker than that with ENSO and AO, and there was a nonsignificant covariance between PDO and extreme temperature events. In addition, the WTC spectra showed that teleconnection factors including solar activity and three large-scale climate phenomena had significant impacts on annual and monthly drought evolution, and AO had the strongest influence on annual standardized precipitation evapotranspiration index (SPEI) values. In general, compared with SSN, ENSO, PDO and AO all showed clear leading effects on precipitation extremes variability and annual streamflow variability for a specific time and frequency, and solar activity’s influences might be transferred by ENSO to precipitation extremes or streamflow variability at the 2–7-year band. Overall, the warming and wetting trend in Xinjiang may be a local manifestation of global multivariate climate change. Thus, our findings will have important implications for designing best practice strategies for water resource management and ecological restoration in similar arid-semiarid basins around the world.