As a test of our unified theory of cosmic rays and high energy astrophysical phenomena, we have calculated the diffuse gamma ray background radiation produced by inverse Compton scattering of cosmic-microwave-background and starlight photons by Galactic and extragalactic cosmic ray electrons. The main sources of such electrons are the highly relativistic jets from supernova explosions and active galactic nuclei. We show that our calculations well reproduce the spectrum and intensity of the diffuse gamma-ray background radiation measured by EGRET in directions away from the Galactic disk and centre.