It has been observed that the Universe is permeated by the cosmic photon background, ranging from radio waves to gamma rays. We investigate the conversion of the photon background into gravitons in the presence of background magnetic fields in the Milky Way Galaxy and in blazar jets. We find that the resulting graviton background is dominated by the contribution generated in blazar jets. Importantly, this graviton background constitutes a graviton floor for high-frequency gravitational wave detectors searching for new physics, analogous to the neutrino floor.