The Abbay River Basin, which originates in Ethiopia, is a major tributary and main source of the Nile River Basin. Land cover and vegetation in the Abbay River Basin is highly susceptible to climate change. This study was conducted to investigate the trends of climate change for a period of thirty-six years (1980–2016) within selected stations of the basin by using the innovative trend analysis method, Mann–Kendall test, and Sen’s slope estimator test to investigate the mean annual precipitation and temperature variables. Changes in land cover and vegetation in the Abbay River Basin were studied for a period of thirteen years (2001–2013) by using remote sensing, GIS analysis, land cover classification, and vegetation detection methods to assess the land cover and vegetation in the basin. In addition, Normalized Difference Vegetation Index (NDVI), Enhanced Vegetation Index (EVI), and Transformation Matrix were employed to analyze the spatial and temporal patterns of land cover and vegetation impacted by changes in climate. The result reflects that the trend of average annual temperature was remarkably increased (Φ = 0.12, Z = 0.75) in the 36-year period, and the temperature was increased by 0.5°C, although precipitation had slightly decreased during the same period. In the thirteen years’ period, forest land and water resource decreased by 3429.62 km2 and 81.45 km2, respectively. In contrast, an increment was observed in grassland (2779.33 km2), cultivated land (535.34 km2), bare land (43.08 km2), urban land (0.65 km2), and wetland (152.66 km2) in the same period. In the study, it was also observed a decrease of an NDVI value by 0.1 was observed in 2013 in the southern part of the basin. The findings of the present study illustrate a significant change in eco-hydrological conditions in the ARB with an adverse impact on the environment. Hydroclimatic changes caused the increase in temperature and decreasing trend in precipitation which significantly impacted the land cover and vegetation in the basin. The changes in land cover were mostly caused by global and local climate influence which mainly affects the hydroclimate and eco-hydrology systems of the basin. The result is consistent with that of the previous studies conducted elsewhere. The findings of this paper could help researchers to understand the eco-hydrological condition of the study basin and become a foundation for further studies.