We demonstrate the generation of extreme-ultraviolet (XUV) free-electron laser (FEL) pulses with time-dependent polarization. To achieve polarization modulation on a femtosecond timescale, we combine two mutually delayed counterrotating circularly polarized subpulses from two cross-polarized undulators. The polarization profile of the pulses is probed by angle-resolved photoemission and above-threshold ionization of helium; the results agree with solutions of the time-dependent Schrödinger equation. The stability limit of the scheme is mainly set by electron-beam energy fluctuations, however, at a level that will not compromise experiments in the XUV. Our results demonstrate the potential to improve the resolution and element selectivity of methods based on polarization shaping and may lead to the development of new coherent control schemes for probing and manipulating core electrons in matter.