To accurately create corneal stromal equivalents with native‐like structure and composition, a new biofunctionalized, curved template is developed that allows the precise orientation of cells and of their extracellular matrix. This template is the first demonstration that curvature alone is sufficient to induce the alignment of human corneal stromal cells, which in turn are able to biofabricate stromal tissue equivalents with cornea‐like shape and composition. Specifically, tissues self‐released from curved templates show a highly organized nanostructure, comprised of aligned collagen fibrils, significantly higher expression of corneal stroma‐characteristic markers keratocan, lumican, decorin, ALDH3, and CHST6 (p = 0.012, 0.033, 0.029, 0.003, and 0.02, respectively), as well as significantly higher elastic modulus (p = 0.0001) compared with their planar counterparts. Moreover, curved tissues are shown to support the growth, stratification, and differentiation of human corneal epithelial cells in vitro, while maintaining their structural integrity and shape without any supporting carriers, scaffolds, or crosslinking agents. Together, these results demonstrate that corneal stromal cells can align and create highly organized, purposeful tissues by the influence of substrate curvature alone, and without the need of additional topographical cues. These findings can be important to further understand the mechanisms of corneal biosynthesis both in vitro and in vivo.