The effect of confined electron-optical phonon interaction on the hydrogenic impurity binding energy in a quantum well is studied. By using the Landau and Pekar variational method, the Hamiltonian is separated into two parts which contain phonon variables and electron variables. A perturbative-variational technique is then employed to construct the trial wave function for the electron part. The effects of electron-optical phonon interaction on the binding energies are calculated as functions of the well width. In the study of the polaron effects on the impurity binding energies in a quantum well, both confined bulk optical phonon and surface optical phonon effects are taken into account. It is found that the surface phonon effect prevails over the bulk phonon effect when the well width is small. The polaron effects on lower-lying excited states are also calculated. The line strengths of transitions from the ground state to lower-lying excited states are calculated as functions of the donor position and the well width.