The coherence of an optical beam having multiple degrees of freedom (DoFs) is described by a coherency matrix G spanning these DoFs. This optical coherency matrix has not been measured in its entirety to date--even in the simplest case of two binary DoFs where G is a 4 × 4 matrix. We establish a methodical yet versatile approach--optical coherency matrix tomography--for reconstructing G that exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. Here G is reconstructed from a minimal set of linearly independent measurements, each a cascade of projective measurements for each DoF. We report the first experimental measurements of the 4 × 4 coherency matrix G associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young's double slit to spatial parity and orbital angular momentum modes.