Invisibility to electromagnetic fields has become an exciting theoretical possibility. However, the experimental realization of electromagnetic cloaks has only been achieved starting from simplified approaches (for instance, based on ray approximation, canceling only some terms of the scattering fields, or hiding a bulge in a plane instead of an object in free space). Here, we demonstrate, directly from Maxwell equations, that a specially designed cylindrical superconductor-ferromagnetic bilayer can exactly cloak uniform static magnetic fields, and we experimentally confirmed this effect in an actual setup.