FRET is widely used for the study of protein-protein interactions in biological samples. However, it is difficult to quantify both the FRET efficiency (E) and the affinity (Kd) of the molecular interaction from intermolecular FRET signals in samples of unknown stoichiometry. Here, we present a method for the simultaneous quantification of the complete set of interaction parameters, including fractions of bound donors and acceptors, local protein concentrations, and dissociation constants, in each image pixel. The method makes use of fluorescence lifetime information from both donor and acceptor molecules and takes advantage of the linear properties of the phasor plot approach. We demonstrate the capability of our method in vitro in a microfluidic device and also in cells, via the determination of the binding affinity between tagged versions of glutathione and glutathione S-transferase, and via the determination of competitor concentration. The potential of the method is explored with simulations.