Engineering a functional replacement for the annulus fibrosus (AF) of the intervertebral disc is contingent upon recapitulation of AF structure, composition, and mechanical properties. In this study, we propose a new paradigm for AF tissue engineering that focuses on the reconstitution of anatomic fiber architecture and uses constitutive modeling to evaluate construct function. A modified electrospinning technique was utilized to generate aligned nanofibrous polymer scaffolds for engineering the basic functional unit of the AF, a single lamella. Scaffolds were tested in uniaxial tension at multiple fiber orientations, demonstrating a nonlinear dependence of modulus on fiber angle that mimicked the nonlinearity and anisotropy of native AF. A homogenization model previously applied to native AF successfully described scaffold mechanical response, and parametric studies demonstrated that nonfibrillar matrix, along with fiber connectivity, are key contributors to tensile mechanics for engineered AF. We demonstrated that AF cells orient themselves along the aligned scaffolds and deposit matrix that contributes to construct mechanics under loading conditions relevant to the in vivo environment. The homogenization model was applied to cell-seeded constructs and provided quantitative measures for the evolution of matrix and interfibrillar interactions. Finally, the model demonstrated that at fiber angles of the AF (28°–44°), engineered material behaved much like native tissue, suggesting that engineered constructs replicate the physiologic behavior of the single AF lamella. Constitutive modeling provides a powerful tool for analysis of engineered AF neo-tissue and native AF tissue alike, highlighting key mechanical design criteria for functional AF tissue engineering.