Morphing wings are expected to have a transformative impact on future transportation and energy systems. To enable the analysis and optimization of morphing wings, efficient numerical models are critically important. In this work, we present an accurate and tractable reduced-order model embedded in a genetic algorithm-based optimization framework. The modeling and optimization framework allows concurrent aerostructural design and flight trajectory optimization of morphing wings considering complete flight missions. The approach is demonstrated on a camber morphing wing airborne wind energy (AWE) system. The system’s power production capability is improved by enabling wing shape changes, and thus adaptation of the aerodynamic properties through morphing at different flight conditions and operating modes. The results of this study highlight the potential of the proposed modeling and optimization approach: 1) the power production capability of the investigated AWE system is improved by 46.0% compared to a sequentially optimized wing design; and 2) by exploiting camber morphing to adapt the aerodynamic properties of the wing at different flight conditions, the power production is further increased by 7.8%.