Theoretical models for the production of relativistic jets from active galactic nuclei predict that jet power arises from the spin and mass of the central black hole, as well as the magnetic field near the event horizon 1 . The physical mechanism mechanism underlying the contribution from the magnetic field is the torque exerted on the rotating black hole by the field amplified by the accreting material. If the squared magnetic field is proportional to the accretion rate, then there will be a correlation between jet power and accretion luminosity. There is evidence for such a correlation 2-8 , but inadequate knowledge of the accretion luminosity of the limited and inhomogeneous used samples prevented a firm conclusion. Here we report an analysis of archival observations of a sample of blazars (quasars whose jets point towards Earth) that overcomes previous limitations. We find a clear correlation between jet power as measured through the γ-ray luminosity, and accretion luminosity as measured by the broad emission lines, with the jet power dominating over the disk luminosity, in agreement with numerical simulations 9 . This implies that the magnetic field threading the black hole horizon reaches the maximum value sustainable by the accreting matter 10 .The jet power is predicted 1 to depend on (aMB) 2 , where a and M are respectively the spin and mass of the black hole and B is the magnetic field at its horizon. Seed magnetic fields are amplified by the accretion disk up to equipartition with the mass energy density ∼ ρc 2 of the matter accreting at the rateṀ . A greaterṀ implies a larger ρ, that can sustain a larger magnetic field, which in turn can tap a larger amount of the black hole rotational energy. The magnetic field is thus a catalyst for the process. Increasing the spin of the black hole shrinks the innermost stable orbit, increasing the accretion efficiency η (defined by η = L disk /Ṁc 2 ) (L disk accretion disk luminosity) to a maximum value 11 η = 0.3.We use a well designed sample of blazars that have been detected in the γ-ray band by the Fermi Large Area Telescope (LAT) that have been spectroscopically observed in the optical 12, 13 (see Methods). They have been classified as BL Lac objects or Flat Spectrum Radio Quasars (FSRQs) according if the rest frame equivalent width of their broad emission lines was greater (FSRQ) or smaller (BL Lacs) than 5Å (rest frame). The sample contains 229 FSRQs, and 475 BL Lacs. Of the latter, 209 have a spectroscopically measured redshift. We considered all FSRQs with enough multi-wavelength data to have a Spectral Energy Distribution (SED) that allows to establish the bolometric luminosity. The considered FSRQs amount to 191 objects. Instead, for BL Lacs, we consider only the 26 sources with detected broad emission lines. This makes them the low disk luminosity tail of of the full 1 blazar sample. This choice is dictated by our will to measure the accretion luminosity, together with the jet power. Through the visible broad emission lines we reconstruct, through a t...