We report on a well-defined peak (the F-line) in photoluminescence (PL) spectra, interpreted as the exciton (D(-)X) bound at the negatively charged donor (the D- state) in GaAs/AlGaAs quantum wells. The F-line exhibits an enhanced intensity with increasing magnetic field due to an increasing wave-function overlap caused by the enhanced localization of the hole and electrons bound at the donor. An enhanced PL intensity together with a red-shift is also observed for the F-line with increasing excitation intensity, i.e. a larger exciton binding energy with increasing intensity. Another characteristic property of the F-line is a very small thermal activation energy. The observed properties of the F-line, with a striking dependence on the excitation intensity, magnetic field and temperature, are all consistent with the observation of the exciton bound at the D- singlet state. Another associated higher-energy peak (the E-line) is observed in PL excitation spectra. The E-line has a similarly strong magnetic field and temperature dependence, and is interpreted as the exciton bound at the D- triplet state.