We present time-resolved 10.4-m GTC and 4.2-m WHT intermediate resolution spectroscopy of the X-ray transient MAXI J1820+070 (=ASASSN-18ey) obtained during its decline to the quiescent state. Cross-correlation of the 21 individual spectra against late-type templates reveals a sinusoidal velocity modulation with a period of 0.68549 +/- 0.00001 d and semi-amplitude of 417.7 +/- 3.9 km/s. We derive a mass function f(M) = 5.18 +/- 0.15 Msun, dynamically confirming the black hole nature of the compact object. Our analysis of the stellar absorption features supports a K3-5 spectral classification for the donor star, which contributes 20% of the total flux at 5200-6800 Angs. The photometric 0.703 +/- 0.003 d periodicity observed during outburst is 2.6% longer than the orbital period supporting the presence of a superhump modulation in the outburst lightcurves. In line with this interpretation, we constrain the binary mass ratio to be q=0.12. In addition, we observe a sharp increase in the Halpha emission line equivalent width during inferior conjunction of the donor star that we interpret as a grazing eclipse of the accretion disc and allows us to constrain the binary inclination to > 69 deg. On the other hand, the absence of X-ray eclipses during outburst imply i < 77 deg. These inclination limits, together with our dynamical solution, lead to a black hole mass in the range 7-8 Msun. We also measure a systemic velocity = -21.6 +/- 2.3 km/s which, combined with the Gaia DR2 proper motion and parallax, implies a large peculiar velocity of 100 km/s.
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