We report the discovery of the likely white dwarf companions to radio millisecond pulsars 47 Tuc Q and 47 Tuc S in the globular cluster 47 Tucanae. These blue stars were found in near-ultraviolet images from the Hubble Space Telescope for which we derived accurate absolute astrometry, and are located at positions consistent with the radio coordinates to within 0.016 arcsec (0.2sigma). We present near-ultraviolet and optical colours for the previously identified companion to millisecond pulsar 47 Tuc U, and we unambiguously confirm the tentative prior identifications of the optical counterparts to 47 Tuc T and 47 Tuc Y. For the latter, we present its radio-timing solution for the first time. We find that all five near-ultraviolet counterparts have U300-B390 colours that are consistent with He white dwarf cooling models for masses ~0.16-0.3 Msun and cooling ages within ~0.1-6 Gyr. The Ha-R625 colours of 47 Tuc U and 47 Tuc T indicate the presence of a strong Ha absorption line, as expected for white dwarfs with an H envelope.