The exciton recombination dynamics is studied experimentally and theoretically in two-monolayer-thick GaAs/AlAs quantum wells characterized by an indirect band gap and a type-II band alignment. At cryogenic temperatures, the lifetimes of the excitons that are indirect both in real and k space are in the millisecond range. The exciton recombination time and the photoluminescence (PL) intensity are strongly dependent on strength and orientation of an applied magnetic field. In contrast to the very weak influence of an in-plane field, at 2 K temperature a field applied parallel to the growth axis drastically slows down the recombination and reduces the PL intensity. With increasing temperature the magnetic field effects on PL intensity and decay time are vanishing. The experimental data are well described by a model for the exciton dynamics that takes into account the magnetic-field-induced redistribution of the indirect excitons between their bright and dark states. It allows us to evaluate the lower bound of the heavy-hole longitudinal g factor of 2.5, the radiative recombination time for the bright excitons of 0.34 ms, and the nonradiative recombination time of the bright and dark excitons of 8.5 ms.