Polarization control is a key feature of light generated by short-wavelength free-electron lasers. In this work, we report the first experimental characterization of the polarization properties of an extreme ultraviolet high gain free-electron laser operated with crossed polarized undulators. We investigate the average degree of polarization and the shot-to-shot stability and we analyze aspects such as existing possibilities for controlling and switching the polarization state of the emitted light. The results are in agreement with predictions based on Gaussian beams propagation.