As climate change intensifies hydroclimatic extremes, advancing drought prediction capabilities has become critical for building resilience in vulnerable agricultural deltas. This urgency is acute in the Mekong Delta, where severe droughts have repeatedly caused profound social and economic damage, underscoring the need for improved forecasting to inform mitigation and preparedness. This study presents an AI-based framework that integrates precipitation moisture diagnostics with deep learning to significantly improve drought prediction in the Vietnamese Mekong Delta (VMD). First, moisture source contributions were quantified by using the Water Accounting Model-2layers (WAM-2layers), a moisture tracking tool with the ERA5 reanalysis data as inputs, revealing that over 60% of VMD precipitation originates from upwind source regions, with humidity and wind speed identified as dominant causal drivers of drought-period deficits. Building on this physical insight, a Convolutional Gated Recurrent Unit (ConvGRU) model was employed and explicitly trained with these external atmospheric variables. The model demonstrated robust multi-type drought forecasting skill at a 3-month lead, accurately detecting ~90% of meteorological and ~80% of agricultural droughts with low false-alarm rates (<10%), and reliably reconstructing major historical drought events. This work establishes a synergistic methodology, in which process-based diagnostics inform and validate an AI-driven prediction system, directly contributing to more reliable, physically interpretable early warning and supporting agricultural resilience and economic stability in this climate-sensitive delta.