The origin of ultra-high-energy cosmic rays (UHECRs) remains an enigma. They offer a window to new physics, including tests of physical laws at energies unattainable by terrestrial accelerators. They must be accelerated locally, otherwise, background radiations would severely suppress the flux of protons and nuclei, at energies above the Greisen-Zatsepin-Kuzmin (GZK) limit. Nearby, gamma ray bursts (GRBs), hypernovae, active galactic nuclei and their flares have all been suggested and debated as possible sources. A local sub-population of type Ibc supernovae (SNe) with mildly relativistic outflows have been detected as sub-energetic GRBs, X-ray flashes and recently as radio afterglows without detected GRB counterparts. Here, we measure the size-magnetic field evolution, baryon loading and energetics, using the observed radio spectra of SN 2009bb. We place such engine-driven SNe above the Hillas line and establish that they can readily explain the post-GZK UHECRs.