The nucleus of the Milky Way is known to harbour regions of intense star formation activity as well as a super-massive black hole. Recent Fermi space telescope observations have revealed regions of gamma-ray emission reaching far above and below the Galactic Centre, the so-called Fermi bubbles. It is uncertain whether these were generated by nuclear star formation or by quasar-like outbursts of the central black hole and no information on the structures magnetic field has been reported. Here we report on the detection of two giant, linearly-polarized radio Lobes, containing three ridge-like sub-structures, emanating from the Galactic Centre. The Lobes each extend ~60 deg, bear a close correspondence to the Fermi bubbles, are located in the Galactic bulge, and are permeated by strong magnetic fields of up to 15 mu G. Our data signal that the radio Lobes originate in a bi-conical, star-formation (rather than black hole) driven outflow from the Galaxys central 200 pc that transports a massive magnetic energy of ~10^55 erg into the Galactic halo. The ridges wind around this outflow and, we suggest, constitute a `phonographic record of nuclear star formation activity over at least 10 Myr.