Effective microstructural properties are critical in determining the electrochemical performance of solid oxide fuel cells (SOFCs), particularly when operating at high current densities. A novel tubular SOFC anode with a hierarchical microstructure, composed of self-organized micro-channels and sponge-like regions, has been fabricated by a phase inversion technique to mitigate concentration losses. However, since pore sizes span over two orders of magnitude, the determination of the effective transport parameters using image-based techniques remains challenging. Pioneering steps are made in this study to characterize and optimize the microstructure by coupling multi-length scale 3D tomography and modeling. The results conclusively show that embedding finger-like micro-channels into the tubular anode can improve the mass transport by 250% and the permeability by 2–3 orders of magnitude. Our parametric study shows that increasing the porosity in the spongy layer beyond 10% enhances the effective transport parameters of the spongy layer at an exponential rate, but linearly for the full anode. For the first time, local and global mass transport properties are correlated to the microstructure, which is of wide interest for rationalizing the design optimization of SOFC electrodes and more generally for hierarchical materials in batteries and membranes.