Solid oxide fuel cells (SOFCs) are a promising technology for producing clean energy in the future. To enhance the efficiency and the lifetime of SOFCs and SOFC stacks, novel materials and innovative material compositions for the constituent layers—namely the cathode, anode, and electrolyte—must be developed. Since the electrodes are of tremendous importance for an efficient and long-term operation, computational methods are required to enable and accelerate the development process. In this work, the microstructure of an SOFC anode is characterised by certain geometrical descriptors, such as the volume fraction, the two-point correlation function, the lineal-path function, the tortuosity, the percolation of each constituent, and the triple phase boundary (TPB). In addition, the effective physical properties are determined by the first-order computational homogenisation method to enable the usage of real anisotropic material parameters in macroscopic fuel cell simulations. Special attention is paid to the mechanical behaviour, including secondary creep. A general framework for creating structure-property relationships for fuel cell electrodes is established. Since it is unfeasible to build large datasets based on experimental tomography images, the microstructure characterisation and reconstruction tool MCRpy is used to generate microstructures based on the geometrical descriptors (i) of the whole three-dimensional tomography image and (ii) of only three two-dimensional slices. A two-step approach is employed with a differentiable microstructure characterisation and reconstruction (DMCR) algorithm and the classical Yeong-Torquato algorithm. The results show a very good agreement of the geometrical and the physical properties between the original tomography image and the reconstructed microstructures. However, to decrease the small differences in the properties, it is necessary to include further geometrical descriptors into the reconstruction process in further research. The created framework can support the development of optimised electrode microstructures using inverse design methods.