Ferromagnet/two-dimensional transition-metal dichalcogenide (FM/2D TMD) interfaces provide attractive opportunities to push magnetic information storage to the atomically thin limit. Existing work has focused on FMs contacted with mechanically exfoliated or chemically vapor-deposition-grown TMDs, where clean interfaces cannot be guaranteed. Here, we report a reliable way to achieve contamination-free interfaces between ferromagnetic CoFeB and molecular-beam epitaxial MoSe2. We show a spin reorientation arising from the interface, leading to a perpendicular magnetic anisotropy (PMA), and reveal the CoFeB/2D MoSe2 interface allowing for the PMA development in a broader CoFeB thickness-range than common systems such as CoFeB/MgO. Using X-ray magnetic circular dichroism analysis, we attribute generation of this PMA to interfacial d-d hybridization and deduce a general rule to enhance its magnitude. We also demonstrate favorable magnetic softness and considerable magnetic moment preserved at the interface and theoretically predict the interfacial band matching for spin filtering. Our work highlights the CoFeB/2D MoSe2 interface as a promising platform for examination of TMD-based spintronic applications and might stimulate further development with other combinations of FM/2D TMD interfaces.