We report on the development of a high-resolution scanning magnetometer, which fully exploits the vectorial nature of the magneto-optical Kerr effect. The three-dimensional nature of magnetization is at the basis of many micromagnetic phenomena and from these data, we can fully characterize magnetization processes of nanostructures in static and dynamic regimes. Our scanning Kerr magnetometer uses a high numerical aperture microscope objective where the incident light beam can be deterministically deviated from the objective symmetry axis, therefore, both in-plane (via the longitudinal Kerr effect) and out-of-plane (via the polar Kerr effect) components of the magnetization vector may be detected. These components are then separated by exploiting the symmetries of the polar and longitudinal Kerr effects. From four consecutive measurements, we are able to directly obtain the three orthogonal components of the magnetization vector with a resolution of 600 nm. Performance of the apparatus is demonstrated by a measurement of 3D magnetization vector maps showing out-of-plane domains and in-plane domain walls in an yttrium-iron-garnet film and on a study of magnetization reversal in a 4-μm-wide magnetic disk.