Understanding the hydrometeorological processes of the Yarlung Tsangpo River Basin, located on the “Third Pole” Qinghai–Tibet Plateau, is crucial for effective water resource management and climate change adaptation. This study provides a comprehensive analysis of the basin’s hydrometeorological characteristics using long-term observational data from six representative stations across the upper, middle, and lower reaches. We examined trends, periodicity, variability, and correlations of key elements—precipitation, temperature, evaporation, and discharge—employing methods such as linear regression, Mann–Kendall tests, wavelet analysis, and Kendall rank correlation coefficient tests. The results indicated that precipitation and discharge exhibited non-significant upward trends, with fluctuations across decades, while temperature showed a significant increase of 0.39 °C per decade, surpassing the national and global rates. Evaporation generally decreased with increasing precipitation; however, at Lazi Station, evaporation significantly increased due to low precipitation and rising temperatures causing decreased relative humidity. Periodic analysis revealed cycles at multiple temporal scales, particularly at 2–5 years, 10 years, and over 20 years. Correlation analysis demonstrated a strong positive relationship between precipitation and discharge, and a negative correlation between evaporation and discharge. The hydrometeorological characteristics are significantly influenced by climatic factors, especially precipitation and temperature, with the warming trend potentially affecting water’s availability and distribution. These findings offer valuable insights for water resource management and highlight the need for continuous monitoring to understand hydrological responses to climatic and anthropogenic changes in this critical region.