A promising new treatment for large and complex bone defects is to implant specifically designed and additively manufactured synthetic bone scaffolds. Optimizing the scaffold design can potentially improve bone in-growth and prevent under- and over-loading of the adjacent tissue. This study aims to optimize synthetic bone scaffolds over multiple-length scales using the full-scale topology optimization approach, and to assess the effectiveness of this approach as an alternative to the currently used mono- and multi-scale optimization approaches for orthopaedic applications. We present a topology optimization formulation, which is matching the scaffold's mechanical properties to the surrounding tissue in compression. The scaffold's porous structure is tuneable to achieve the desired morphological properties to enhance bone in-growth. The proposed approach is demonstrated in-silico, using PEEK, cortical bone and titanium material properties in a 2D parameter study and on 3D designs. Full-scale topology optimization indicates a design improvement of 81% compared to the multi-scale approach. Furthermore, 3D designs for PEEK and titanium are additively manufactured to test the applicability of the method. With further development, the full-scale topology optimization approach is anticipated to offer a more effective alternative for optimizing orthopaedic structures compared to the currently used multi-scale methods.