We investigated the interdiffusion of InGaAs/InP quantum wells (QWs) due to rapid thermal annealing (RTA) by photoluminescence (PL) spectroscopy and wedge transmission electron microscopy (WTEM). After RTA at temperatures between 650 and 900 degrees C (annealing time 1 min) we observed large emission energy shifts of up to 210 meV. From the temperature dependence of the PL emission energy shifts, the interdiffusion lengths, interdiffusion coefficients and activation energies (e.g. of 2 eV) were determined using a simple model of ion intermixing. In addition the samples were characterized by WTEM to obtain a microscopic understanding of the interdiffusion process across the InGaAs-InP heterostructure interface. We obtained a transition region length of about 2.5 nm for an 11 nm QW, in qualitative agreement with the interdiffusion length obtained from PL spectroscopy. From WTEM analysis the variation in chemical composition across the interface was determined, suggesting lattice-matched interdiffusion.