Appropriate load‐bearing function of soft connective tissues is provided by their nonlinear and often anisotropic mechanics. Recapitulating such complex mechanical behavior in tissue‐engineered structures is particularly crucial, as deviation from native tissue mechanics can trigger pathological biomechanical pathways, causing adverse tissue remodeling and dysfunction. Here, a novel method combining computational modeling, melt electrowriting (MEW), and design of experiments (DOE) is reported to generate scaffolds composed of sinusoidal fibers with prescribed biaxial mechanical properties, recapitulating the distinct nonlinear, anisotropic stress–strain behavior of three model tissues: adult aortic valve, pediatric pulmonary valve, and pediatric pericardium. Finite element analysis is used to efficiently optimize scaffold architecture over a broad parameter space, representing up to 65 conditions, to define MEW print parameters to achieve polycaprolactone scaffolds with target mechanical properties. Architectural parameters are further optimized experimentally using DOE and regression to account for uncertainties involved in the simulation, yielding functional scaffolds with accurate, prescribed mechanics. The prescribed architecture also primarily governs the mechanics of hybrid structures generated by casting cell‐laden fibrin hydrogel within the scaffolds. This high‐fidelity approach recapitulates biaxial mechanical properties over a broad range of mechanical nonlinearity and anisotropy and is generalizable for programmed biofabrication in a variety of tissue engineering applications.