We reconstruct for the first time the three dimensional structure of magnetic fields on cosmological scales, which were seeded by density perturbations during the radiation dominated epoch of the Universe and later on were evolved by structure formation. To achieve this goal, we rely on three dimensional initial density fields inferred from the 2M++ galaxy compilation via the Bayesian BORG algorithm. Using those, we estimate the magnetogenesis by the so called Harrison mechanism. This effect produced magnetic fields exploiting the different photon drag on electrons and ions in vortical motions, which are exited due to second order perturbation effects in the Early Universe. Subsequently we study the evolution of these seed fields through the non- linear cosmic structure formation by virtue of a magneto-hydrodynamics simulation to obtain a 3D estimate for the structure of this primordial magnetic field component today. At recombination we obtain large scale magnetic field strengths around 10(-23) G, with a power spectrum peaking at about 2 Mpc(-1) h in comoving scales. At present we expect this evolved primordial field to have strengths above approximate to 10(-27) G and approximate to 10(-29) G in clusters of galaxies and voids, respectively. We also calculate the corresponding Faraday rotation measure map and show the magnetic field morphology and strength for specific objects of the Local Universe. These results provide a reliable lower limit on the primordial component of the magnetic fields in these structures.