Appropriate load-bearing function of soft connective tissues is provided by their nonlinear and often anisotropic mechanical properties. Recapitulating this complex mechanical behaviour in tissue-engineered structures is particularly crucial, as deviation from normal native tissue mechanics can trigger pathological biomechanical pathways, leading to adverse tissue remodelling and dysfunction. Here we report a novel method combining computational modelling, melt electrowriting (MEW), and design of experiments (DOE) to generate scaffolds composed of sinusoidal fibres with prescribed biaxial tensile mechanical properties, recapitulating the distinct nonlinear, anisotropic stress-strain behaviour of three model soft connective tissues: adult aortic valve, pediatric pulmonary valve, and pediatric pericardium. The fibrous scaffolds were fabricated using MEW of polycaprolactone, and their architectures were optimized using DOE and regression models for superior control over scaffold architecture to yield prescribed mechanics. Cell-laden fibrin hydrogel was cast within the fibrous scaffolds to generate hybrid tissue sheets, suitable for connective tissue engineering. The composition of the cell-laden hydrogel and its cell density were optimized to cause minimal contraction, support high cell viability and growth, and minimally contribute to the hybrid tissue biaxial mechanical properties, which were governed by the prescribed MEW scaffold architecture. This high-fidelity approach recapitulates biaxial mechanical properties over a broad range of mechanical nonlinearity and anisotropy and is generalizable for programmed fabrication in a variety of textile, biomaterial, and tissue engineering applications.