Using the Weyl-van der Waerden formalism, we have calculated the polarized amplitudes for e+ e- --> W+ W--gamma with the W bosons on mass shell. Concise analytical formulae are presented for non-collinear photon emission. By a simple extension, our formulae also describe collinear photon emission. Numerical evaluations have been done for energies between 200 GeV and 2 TeV and comparisons with previous numerical results have been performed. This completes the O(alpha) calculation for W-pair production for on-shell W's.