The effects of both electric and magnetic fields on the transition energies between the 1s-like ground state and 2${\mathit{p}}_{\ifmmode\pm\else\textpm\fi{}}$ excited states of hydrogenic donors in a GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum well are studied. The effective-mass approximation within a variational scheme is adopted with electric and magnetic fields considered in the growth direction of the heterostructure, and treated directly in the variational calculation. Results for the finite-barrier potential are obtained as functions of both applied fields and for different GaAs-${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum-well thicknesses, and compared with available infrared magnetospectroscopy measurements on donor-doped quantum wells. Theoretical results indicate that a detailed study of the intradonor absorption spectra together with a proper consideration of the impurity-doping profile are necessary for a qualitative understanding of the experimental results.