This study presents a geographical and temporal analysis of drought in the Tigris-Euphrates Basin from 1960 to 2023, utilizing the high-resolution TerraClimate dataset. Two primary drought indices, the Standardized Precipitation Index (SPI) and the Standardized Precipitation-Evapotranspiration Index (SPEI), were employed to assess the dynamics of meteorological and hydrological droughts. The results indicate an increased intensity and frequency of drought events, especially after the year 1990. The SPEI index highlights the critical negative impact of increased evapotranspiration on the climatological soil-water balance due to the increased evaporative demand as a function of the increased air temperatures in the study region. SPI analyses revealed that changes in precipitation patterns have increased over time, resulting in more frequent regional drought events. SPEI, on the other hand, reflects the drought trend and drought severity more precisely because it takes into account the increasing trend in evapotranspiration as a function of rising air temperatures. SPI and SPEI provided insights into long-term hydrological drought patterns, emphasizing the need for region-specific drought mitigation and adaptation strategies. These findings underscore the value of integrated drought monitoring and assessment for water management and climate adaptation planning in semi-arid and dry sub-humid regions.