Intraexcitonic energy transitions are calculated for hydrogenic exciton states in GaAs quantum wells within a variational scheme in the effective-mass approximation and using an infinite-confinement potential model. In the first part we present the binding energies of the heavy and light-hole exciton ground and excited states with wave functions taken as products of the electron and hole wave functions in the quantum well and the three-dimensional nonseparable hydrogenic wave function. For very small values of width, our results reproduce the exact two-dimensional hydrogenic limit and conversely, for wide wells, we recover the exact three-dimensional results. The binding energy is calculated for the exciton states 1s, 2s, 2px, 2pz, 3s, 3px, and 3pz. The allowed transitions for these excitonic states obey the selection rules for an hydrogenic atom. In addition, we study the expectation values for the electron–hole distance in the direction of the well and in the transverse direction.