Two-dimensional (2D) Fourier-transform optical spectroscopy is demonstrated on GaAs quantum wells. This technique represents a highly enhanced version of transient four-wave mixing (FWM). The 2D spectra are generated by measuring four-wave mixing signal fields as a function of the time after the third pulse and the time delay between the first two excitation pulses. Signal fields are measured, including phase information, by spectral interferometry. Active stabilization of the interferometer allows us to measure the phase of the emitted signal as a function of the phase between the first two excitation pulses. This enables the implementation of the Fourier transform analysis. Our spectra show the light-hole and heavy-hole exciton transitions on the main diagonal as well as coupling between those two levels as off-diagonal peaks.