Due to the cold climate and dramatically undulating altitude, the identification of dynamic vegetation trends and main drivers is essential to maintain the ecological balance in Tibet. The normalized difference vegetation index (NDVI), as the most commonly used greenness index, can effectively evaluate vegetation health and spatial patterns. MODIS-NDVI (Moderate-resolution Imaging Spectroradiometer-NDVI) data for Tibet from 2001 to 2020 were obtained and preprocessed on the Google Earth Engine (GEE) cloud platform. The Theil–Sen median method and Mann–Kendall test method were employed to investigate dynamic NDVI changes, and the Hurst exponent was used to predict future vegetation trends. In addition, the main drivers of NDVI changes were analyzed. The results indicated that (1) the vegetation NDVI in Tibet significantly increased from 2001 to 2020, and the annual average NDVI value fluctuated between 0.31 and 0.34 at an increase rate of 0.0007 year−1; (2) the vegetation improvement area accounted for the largest share of the study area at 56.6%, followed by stable unchanged and degraded areas, with proportions of 27.5 and 15.9%, respectively. The overall variation coefficient of the NDVI in Tibet was low, with a mean value of 0.13; (3) The mean value of the Hurst exponent was 0.53, and the area of continuously improving regions accounted for 41.2% of the study area, indicating that the vegetation change trend was continuous in most areas; (4) The NDVI in Tibet indicated a high degree of spatial agglomeration. However, there existed obvious differences in the spatial distribution of NDVI aggregation areas, and the aggregation types mainly included the high-high and low-low types; and (5) Precipitation and population growth significantly contributed to vegetation cover improvement in western Tibet. In addition, the use of the GEE to obtain remote sensing data combined with time-series data analysis provides the potential to quickly obtain large-scale vegetation change trends.