The magneto-optical Kerr effect (MOKE) is a widely used lab-based technique for the study of thin films and nanostructures, providing magnetic characterization with good spatial and temporal resolutions. Due to the complex coupling of light with a magnetic sample, conventional MOKE magnetometers normally work by selecting a small range of incident wave-vector values, focusing the incident light beam to a small spot, and recording the reflected intensity at that angular range by means of photodetectors. This generally provides signals proportional to a mixture of magnetization components, requiring additional methodologies for full vectorial magnetic characterization. Here, we computationally investigate a Fourier-space MOKE setup, where a focused beam ellipsometer using high numerical aperture optics and a camera detector is employed to simultaneously map the intensity distribution for a wide range of incident and reflected wave-vectors. We employ circularly incident polarized light and no analyzing optics, in combination with a fitting procedure of the light intensity maps to the analytical expression of the Kerr effect under linear approximation. In this way, we are able to retrieve the three unknown components of the magnetization vector as well as the material's optical and magneto-optical constants with high accuracy and short acquisition times, with the possibility of single shot measurements. Fourier MOKE is thus proposed as a powerful method to perform generalized magneto-optical ellipsometry for a wide range of magnetic materials and devices.