Freshwater scarcity in coastal regions such as Port Sudan has become a persistent constraint driven by population growth, climate variability, and infrastructure limitations. While seawater desalination offers a technically viable solution, its implementation is often constrained by high energy requirements and operational costs. This study presents the complete engineering design and techno-economic evaluation of a seawater reverse osmosis (SWRO) desalination system powered by photovoltaic (PV) energy under Red Sea conditions. The system is designed for a production capacity of 10,000 m³/day, incorporating detailed modeling of osmotic pressure, mass balance, hydraulic energy requirements, and photovoltaic power generation. The elevated salinity of the Red Sea (~40 ppt) results in an osmotic pressure of approximately 33.9 bar, requiring an operating pressure near 60 bar. The total energy demand is estimated at 12.78 GWh annually, supplied by a 7.8 MW photovoltaic system based on local solar irradiance data. Economic analysis indicates a capital cost of approximately 22 million USD and a levelized cost of water (LCOW) of 0.66 USD/m³, with a positive net present value over the project lifetime. In addition, the system achieves a significant reduction in carbon emissions compared to conventional fossil-fuel-based desalination. The results confirm that photovoltaic-powered desalination provides a technically feasible and economically sustainable solution for water supply in arid coastal environments.