We present calculations of exciton binding energies in quantum wells under transverse magnetic field. We calculate the free carrier wavefunctions under magnetic field by our recently developed theory. We express the exciton wave-function in terms of the product of a variational envelope function and the free carrier wavefunctions, and obtain the binding energies by variational method. We apply the theory to the 1S heavy hole exciton of InGaAs/GaAs strained quantum wells and calculate diamagnetic shift of the exciton with the band offset rule DELTAE(v)/DELTAEg = 0.48. We find that the results agree very well with the photoluminescence experiment of Hou et al., supporting both the appropriateness of our exciton theory and the band offset rule for this system.