Magnetic nanoparticles are of immense current interest because of their possible use in biomedical and technological applications. Here we demonstrate that the large magnetic anisotropy of FePt nanoparticles can be significantly modified by surface design. We employ X-ray absorption spectroscopy offering an element-specific approach to magnetocrystalline anisotropy and the orbital magnetism. Experimental results on oxide-free FePt nanoparticles embedded in Al are compared with large-scale density functional theory calculations of the geometric- and spin-resolved electronic structure, which only recently have become possible on world-leading supercomputer architectures. The combination of both approaches yields a more detailed understanding that may open new ways for a microscopic design of magnetic nanoparticles and allows us to present three rules to achieve desired magnetic properties. In addition, concrete suggestions of capping materials for FePt nanoparticles are given for tailoring both magnetocrystalline anisotropy and magnetic moments.