One synthetic modality for materials discovery proceeds by forming mixtures of two or more compounds. In transition metal oxides (TMOs), chemical substitution often obeys Vegard's principle, and the resulting structure and properties of the derived phase follow from its components. A change in the assembly of the components into a digital nanostructure, however, can stabilize new polymorphs and properties not observed in the constituents. Here we formulate and demonstrate a crystal chemistry design approach for realizing digital TMOs without inversion symmetry by combining two centrosymmetric compounds, utilizing periodic anion-vacancy order to generate multiple polyhedra that together with cation order produce a polar structure. We next apply this strategy to two brownmillerite-structured TMOs known to display centrosymmetric crystal structures in their bulk, Ca2Fe2O5 and Sr2Fe2O5. We then realize epitaxial (SrFeO2.5)(1)/(CaFeO2.5)(1) thin film superlattices possessing both anion-vacancy order and Sr and Ca chemical order at the subnanometer scale, confirmed through synchrotron-based diffraction and aberration corrected electron microscopy. Through a detailed symmetry analysis and density functional theory calculations, we show that A-site cation ordering lifts inversion symmetry in the superlattice and produces a polar compound. Our results demonstrate how control of anion and cation order at the nanoscale can be utilized to produce acentric structures markedly different than their constituents and open a path toward novel structure-based property design.