Load-bearing systems (structures) in buildings and infrastructure contribute to a significant share of adverse environmental impacts (EI) because of resource- and energy-intensive fabrication. A currently overlooked circular economy strategy to reduce EI is to reuse structural components over multiple service cycles, which avoids resource use, energy for reprocessing, and waste. To apply reuse, the design process is fundamentally different to conventional practice: employing reused elements involves solving an inverse process whereby the structure layout (topology and geometry) is a result of available element characteristics (cross-sections and lengths). This thesis proposes a new computational workflow to enable design through reuse in structural engineering. Discrete structural optimization techniques are formulated to design reticular structures (trusses and frames) that make best use of a stock of reclaimed elements (linear bars and beams). The objective is the minimization of EI through optimizing stock element assignment and structure topology subject to ultimate and serviceability limit states. The structure EI is quantified through Life Cycle Assessment (LCA) which includes process impacts for building deconstruction, reconditioning, and transport of reclaimed elements. The design process is formulated as a Mixed-Integer Linear Programming problem which produces global optima, and thus it allows rigorous benchmarking between solutions obtained by varying stock compositions and LCA parameters. In addition, geometry optimization is carried out in sequence with assignment optimization to improve further the structure performance and to reduce cut-off waste. The proposed method is applied to typical engineering structures including roof trusses and multi-story building frames subject to statistically simulated and realistic stocks inventoried from deconstructed buildings. Results show that solutions made from reused steel elements have an up to 60% lower EI compared to minimum-weight solutions made of recycled steel elements. An LCA parametric study shows that long transport distances for reclaimed elements are only marginally important, whereas machine operation during deconstruction has a significant influence on EI. This study concludes that a combination of reused and new elements leads to structures with the least EI. To further extend the application range of component reuse, another method is formulated to synthesize a kit of parts comprising linear bars and spherical joints that can be assembled to form non-modular structures of diverse layouts. Multiple structure geometries are optimized simultaneously with the kit-of-parts composition (number of elements, dimensions, cross-sections). The method is implemented as an interactive design and fabrication workflow which has been successfully applied to build three pavilion-scale prototypes. Results show that reusability of the same set of components for multiple structures requires only half the components compared to one-off construction. In summary, this thesis lays out the foundation for optimum design of structures through component reuse and it provides new benchmarks of attainable EI reductions compared to structures made of new components. The significant EI reduction obtained through applying the proposed workflow fosters a broader implementation of reuse strategies in research and practice.