Magneto-optics of low dimensional semiconductors, such as monolayer transition metal dichalcogenides, offers a vast playground for exploring complex quantum phenomena. However, current ab initio approaches fail to capture important experimental observations related to brightening of excitonic levels and their g-factor dependence. Here, we develop a robust and general first principles framework for many-body exciton g-factors by incorporating off-diagonal terms for the spin and orbital angular momenta of single-particle bands and many-body states for magnetic fields pointing in arbitrary spatial directions. We implement our framework using many-body perturbation theory via the GW-Bethe-Salpeter equation (BSE) and supplement our analysis with robust symmetry-based models, establishing a fruitful synergy between many-body GW-BSE and group theory. Focusing on the archetypal monolayer WSe_2, we accurately reproduce the known results of the low-energy excitons including the Zeeman splitting and the dark/grey exciton brightening. Furthermore, our theory naturally reveals fundamental physical mechanisms of magnetic-field hybridization of higher-energy excitons (s- and p-like) and resolves the long-standing puzzle of the experimentally measured non-monotonic Rydberg series (1s-4s) of exciton g-factors. Our framework offers a comprehensive approach to investigate, rationalize, and predict the non-trivial interplay between magnetic fields, angular momenta, and many-body exciton physics in van der Waals systems.