Climate change increasingly affects vegetation dynamics and ecosystem health worldwide. This study investigates historical and projected vegetation dynamics in Ethiopia using the Normalized Difference Vegetation Index (NDVI) to assess spatial and temporal patterns of vegetation change and their relationship with climate variability. Seasonal NDVI climatology, anomalies, trends, and future projections were analyzed using AVHRR and MODIS satellite datasets combined with CMIP6 climate projections. Google Earth Engine (GEE) JavaScript workflows were employed to examine vegetation dynamics during the October--January (ONDJ), February--May (FMAM), and June--September (JJAS) seasons from 1991 to 2024 and to project NDVI changes for 2015--2100 under SSP2-4.5 and SSP5-8.5 scenarios. Regression analysis evaluated climate--NDVI relationships, while the Mann--Kendall test and Sen's slope estimator determined the significance and magnitude of vegetation trends. Results reveal substantial spatial variability in vegetation dynamics. Significant NDVI increases occurred in many highland regions, whereas declines were observed in drought-prone areas, particularly in eastern Ethiopia and the Afar region. Decadal analyses (1991--2000, 2001--2010, 2011--2024) showed enhanced vegetation across northern, western, central, and southern Ethiopia, reflecting the combined influence of rainfall variability, climatic extremes, topography, and land cover. Future projections indicate moderate NDVI changes under SSP2-4.5 and greater spatial variability under SSP5-8.5, with potential greening in northern, western, central, and southwestern Ethiopia, and persistent vegetation stress in eastern and Afar areas. The study demonstrates the effectiveness of GEE for large-scale vegetation monitoring and provides valuable information for drought early-warning systems, climate-resilient agricultural planning, and ecosystem management in Ethiopia.