We report the experimental observation of radiative recombination from Rydberg excitons in a two-dimensional semiconductor, monolayer WSe2, encapsulated in hexagonal boron nitride. Excitonic emission up to the 4s excited state is directly observed in photoluminescence spectroscopy in an out-of-plane magnetic field up to 31 T. We confirm the progressively larger exciton size for higher energy excited states through diamagnetic shift measurements. This also enables us to estimate the 1s exciton binding energy to be about 170 meV, which is significantly smaller than most previous reports. The Zeeman shift of the 1s to 3s states, from both luminescence and absorption measurements, exhibits a monotonic increase of the g-factor, reflecting nontrivial magnetic-dipole-moment differences between ground and excited exciton states. This systematic evolution of magnetic dipole moments is theoretically explained from the spreading of the Rydberg states in momentum space.