Nanocomposite materials filled with nanoparticles currently exhibit two important unsolved experimental challenges: (i) the elaboration of a general strategy allowing to finely tune, for an easy-to-tune range of parameters, the anisotropy of nanoparticle assembly inside a polymer matrix for improved anisotropic mechanical reinforcement and (ii) an experimental demonstration establishing that the macroscopic mechanical properties of the materials are quantitatively controlled by the filler microstructure. We address them both here by showing how the versatile bottom-up organization of spherical magnetic nanoparticles controlled by a moderate external magnetic field during processing, enables to obtain a wide variety of anisotropic structures, from quasi-isotropic up to a homogeneous dispersion of aligned chains of nanoparticles, as shown by a refined structural study combining SAXS and TEM experiments. The resulting anisotropy of the mechanical properties is spectacular relative to the low particle volume fraction. The Young modulus can be more than 3 times higher when the bulk material is stretched parallel as opposed to perpendicular to the chains and correlates quantitatively in a proportional manner with the anisotropy of the microstructure.