Diffusion-weighted imaging (DWI) provides information that allows the estimation of white-matter (WM) fibre orientation and distribution, but it does not provide information about myelin density, fibre concentration or fibre size within each voxel. On the other hand, quantitative relaxation contrasts (like the apparent transverse relaxation, R2∗) offer iron and myelin-related contrast, but their dependence on the orientation of microstructure with respect to the applied magnetic field, B0 , is often neglected. The aim of this work was to combine the fibre orientation information retrieved from the DWI acquisition and the sensitivity to microstructural information from quantitative relaxation parameters. The in vivo measured quantitative transverse relaxation maps (R2 and R2∗) were decomposed into their orientation-dependent and independent components, using the DWI fibre orientation information as prior knowledge. The analysis focused on major WM fibre bundles such as the forceps major (FMj), forceps minor (FMn), cingulum (CG) and corticospinal tracts (CST). The orientation-dependent R2 parameters, despite their small size (0-1.5 Hz), showed higher variability across different fibre populations, while those derived from R2∗, although larger (3.1-4.5 Hz), were mostly bundle-independent. With this article, we have, for the first time, attempted the in vivo characterization of the orientation-(in)dependent components of the transverse relaxation rates and demonstrated that the orientation of WM fibres influences both R2 and R2∗ contrasts.