Supermassive black holes (SMBHs) are the central engines of luminous quasars and are found in most massive galaxies today. But the recent discoveries of ULAS J1120+0641, a 2×109 M⊙ BH at z= 7.1, and ULAS J1342+0928, a 8.0×108 M⊙ BH at z= 7.5, now push the era of quasar formation up to just 690 Myr after the Big Bang. Here we report new cosmological simulations of SMBHs with X-rays fully coupled to primordial chemistry and hydrodynamics that show that J1120 and J1342 can form from direct collapse black holes (DCBHs) if their growth is fed by cold, dense accretion streams, like those thought to fuel rapid star formation in some galaxies at later epochs. Our models reproduce all of the observed properties of J1120: its mass, luminosity, and H II region as well as star formation rates and metallicities in its host galaxy. They also reproduce the dynamical mass of the innermost 1.5 kpc of its emission region recently measured by ALMA and J-band magnitudes that are in good agreement with those found by the VISTA Hemisphere Survey.