We report the results of our microstructural investigations into the origin of in-plane uniaxial magnetic anisotropies induced in Ni and Fe thin films by low energy ion beam assisted deposition. 1000 Å films were prepared by ion beam sputtering onto amorphous silica substrates under simultaneous bombardment by 100 eV Xe+ ions under an oblique angle of incidence. The induced anisotropy is studied as a function of ion-to-adsorbate atom arrival ratio, R, from values of 0 to 0.35. The maximum anisotropy field is 150 Oe for Ni and 80 Oe for Fe, but their hard axes are oriented orthogonal to each other. Asymmetric x-ray diffraction is employed to study both in-plane and out-of-plane lattice spacings and crystallographic orientation. In agreement with previous work, we find evidence of a anisotropic in-plane strain of magnitude 0.2-0.5%. In all films, the direction perpendicular to the ion bombardment is compressed relative to parallel. The uniaxial magnetic anisotropy is correlated with this in-plane anisotropic strain using a simple magnetoelastic model.