Heating the outer layers of the magnetically quiet solar atmosphere to more than one million kelvin and accelerating the solar wind requires an energy flux of approximately 100 to 300 watts per square metre(1-6), but how this energy is transferred and dissipated there is a puzzle and several alternative solutions have been proposed. Braiding and twisting of magnetic field structures, which is caused by the convective flows at the solar surface, was suggested as an efficient mechanism for atmospheric heating(7). Convectively driven vortex flows that harbour magnetic fields are observed(8-10) to be abundant in the photosphere (the visible surface of the Sun). Recently, corresponding swirling motions have been discovered(11) in the chromosphere, the atmospheric layer sandwiched between the photosphere and the corona. Here we report the imprints of these chromospheric swirls in the transition region and low corona, and identify them as observational signatures of rapidly rotating magnetic structures. These ubiquitous structures, which resemble super-tornadoes under solar conditions, reach from the convection zone into the upper solar atmosphere and provide an alternative mechanism for channelling energy from the lower into the upper solar atmosphere.