We report on the observation of a significant increase of the radiative decay rates for exciton transitions in a wide (In,Ga)As/GaAs quantum well (L=95 nm) in magnetic fields up to 6 T applied along the growth axis of the heterostructure. The absolute values of the radiative decay rates are obtained from a quantitative analysis of resonant features in the experimentally measured reflectance spectra in the range of the optical transitions to the quantum-confined exciton states. High crystalline quality of the heterostructure allows us to observe the ground and several excited exciton transitions with the nonradiative broadening comparable to the radiative one. We employ a numerical procedure appropriate for the studied wide quantum well to model the increase of the radiative decay rate in magnetic field. The results of the modeling agree well with the experimental data.