In arid regions of Asia and Africa, where evaporative demand exerts increasing control over drought dynamics under climate change, this study introduces the Evaporative Demand Drought Index (EDDI) as a complementary tool to precipitation-based indices for improved monitoring of flash droughts and evapotranspiration-driven moisture stress. Using ERA5-Land reanalysis data at 0.1 degrees resolution, EDDI was calculated using the PenmanMonteith formulation across timescales from sub-weekly to 12 months period. Its performance was evaluated against the Standardized Precipitation Index (SPI) and Standardized Precipitation-Evapotranspiration Index (SPEI) through modified Mann-Kendall trend analysis, Sen's slope estimation, Spearman rank correlations, run theory-based drought characterization, and a detailed examination of the 2010 drought event. EDDI showed strong inverse correlations with SPI and SPEI (ranging from -0.41 to -0.91), with the strongest association, -0.91, observed between EDDI and SPEI at the 1-month scale in the Sahara (SAH) region. Across the studied arid domains, EDDI revealed more pronounced drying trends than those identified by SPI or SPEI, attributable to significant increases in temperature (0.02-0.05 degrees C year- 1) and reference evapotranspiration (ETo) (2.0-5.16 mm year- 1). Drought frequency intensified in most regions after 2000, except on the Tibetan Plateau (TIB). During the 2010 drought episode, EDDI detected the onset of the drought weeks earlier than SPI, demonstrating its sensitivity to rapid increases in evaporative demand. These findings indicate that EDDI serves as a valuable complementary index, capturing aspects of drought related to atmospheric evaporative demand and rapid-onset events that may be underrepresented by precipitation-focused metrics. Integrating EDDI into operational drought early warning systems for arid regions could enhance monitoring capabilities and support more informed decision-making for drought risk management under ongoing climate change.