The Ly α lines of H I and He II are two of the spectral lines of choice for FUV and EUV channels of narrowband imagers on board sounding rockets and space telescopes, which provide spectacular intensity images of the outer solar atmosphere. Since the magnetic field information is encoded in the polarization of the spectral line radiation, it is important to investigate whether the ensuing Ly α radiation from the solar disk can be polarized, along with its magnetic sensitivity. Here we present some theoretical predictions concerning the amplitudes and magnetic sensitivities of the linear polarization signals produced by scattering processes in these strong emission lines of the solar transition region, taking into account radiative transfer and the Hanle effect caused by the presence of organized and random magnetic fields. We find that the line-center amplitudes of the fractional polarization signals vary typically between a fraction of a percent and ˜1%, depending on the Ly α line under consideration, the scattering geometry and the strength and orientation of the magnetic field. Interestingly, while the Ly α line of He II starts to be sensitive to the Hanle effect for magnetic strengths B>̰100 G the hydrogen Lyα line is mainly sensitive to magnetic strengths between 10 and 100 G. These results encourage the development of FUV and EUV polarimeters for sounding rockets and space telescopes with the aim of opening up a diagnostic window for magnetic field measurements in the upper chromosphere and transition region of the Sun.