The primary objective of the KATRIN experiment is to probe the absolute neutrino mass scale with a sensitivity of 200 meV (90% C.L.) by precision spectroscopy of tritium β-decay. To achieve this, a low background of the order of 10−2 cps in the region of the tritium β-decay endpoint is required. Measurements with an electrostatic retarding spectrometer have revealed that electrons, arising from nuclear decays in the volume of the spectrometer, are stored over long time periods and thereby act as a major source of background exceeding this limit. In this paper we present a novel active background reduction method based on stochastic heating of stored electrons by the well-known process of electron cyclotron resonance (ECR). A successful proof-of-principle of the ECR technique was demonstrated in test measurements at the KATRIN prespectrometer, yielding a large reduction of the background rate. In addition, we have carried out extensive Monte Carlo simulations to reveal the potential of the ECR technique to remove all trapped electrons in a few ms with negligible loss of measurement time in the main spectrometer. This would allow the KATRIN experiment attaining its full physics potential.