We present the results of spectropolarimetry of radio galaxies with redshift close to 1, complemented by imaging polarimetry. These show: (1) a flat (in f(lambda)) polarized UV continuum, (2) broad polarized Mg II emission fine, (3) narrow unpolarized forbidden emission lines, (4) a drop in the polarization of the continuum to the red of 4000 angstrom, (5) a strong absorption feature at 2598 angstrom, and (6) perpendicularity between the E vector of polarization, as measured with imaging polarimetry, and the optical/radio axis. These data provide evidence that distant radio galaxies harbor a quasar which is hidden from direct view but seen by scattering from the interstellar medium in the galaxy. Hot electrons cannot be the dominant scattering agent because of the presence of polarized Mg II lines with a width similar to that observed in quasars. The drop in the continuum polarization to the red of the 4000 angstrom break suggests dilution by a red stellar population. The absorption line at 2598 angstrom is probably due to interstellar Fe II. We discuss a two-component model consisting of a dust scattered quasar and an evolved stellar population, which reproduces simultaneously the polarization measurements and the UV/optical spectral energy distribution. Our results provide strong observational support to the unified model for the most luminous active galactic nuclei and to the idea that the alignment effect in distant radio galaxies is due to scattering, and they add an important tool for the study of the early evolution of galaxies.