Agricultural communities in drought-prone regions face escalating climate risks that threaten food security and rural livelihoods, yet traditional indemnity-based insurance remains prohibitively expensive and operationally infeasible for smallholder farmers. This review examines the transformative integration of satellite remote sensing technologies with algorithmic micro-insurance models designed to mitigate drought-related agricultural losses through automated, data-driven financial mechanisms. We synthesize current methodologies for satellite-derived drought indices, vegetation health monitoring, soil moisture estimation, and yield prediction algorithms that underpin index-based and parametric insurance frameworks. Core satellite platforms including Landsat, Sentinel, MODIS, and synthetic aperture radar systems provide multi-temporal, high-resolution earth observation data enabling precise risk quantification at field and regional scales. Operational deployment models demonstrate how normalized difference vegetation index, soil moisture anomalies, evapotranspiration deficits, and precipitation estimates serve as objective triggers for automated payouts, reducing basis risk and transaction costs. Case studies from Sub-Saharan Africa, South Asia, and Latin America reveal significant potential for scalability, though challenges persist regarding data latency, farmer digital literacy, and integration with existing agricultural extension systems. Future directions emphasize enhanced satellite constellation coverage, machine learning-enhanced risk modeling, blockchain-enabled smart contracts, and policy frameworks that embed satellite-driven insurance within broader climate adaptation strategies for vulnerable agricultural populations.