The gamma-ray burst (GRB) jet powers the afterglow emission by shocking the surrounding medium, and radio afterglow can now be routinely observed to almost a year after the explosion. Long-duration GRBs are accompanied by supernovae (SNe) that typically contain much more energy than the GRB jet. Here we consider the fact that the SN blast wave will also produce its own afterglow (supernova remnant emission), which will peak at much later time (since it is non-relativistic), when the SN blast wave transitions from a coasting phase to a decelerating Sedov-Taylor phase. We predict that this component will peak generally a few tens of years after the explosion and it will outshine the GRB powered afterglow well-before its peak emission. In the case of GRB 030329, where the external density is constrained by the $\sim 10$-year coverage of the radio GRB afterglow, the radio emission is predicted to start rising over the next decade and to continue to increase for the following decades up to a level of $\sim$ mJy. Detection of the SN-powered radio emission will greatly advance our knowledge of particle acceleration in $ \sim 0.1$c shocks.