We present two contiguous nights of simultaneous time-resolved Gran Telescopio Canarias spectroscopy and William Herschel Telescope photometry of the black hole X-ray transient XTE J1859+226, obtained in 2017 July during quiescence. Cross-correlation of the individual spectra against a late K-type spectral template enabled us to constrain the orbital period to 0.276 ± 0.003 d and the radial velocity semi-amplitude of the donor star to K2 = 550 ± 59 km s-1. An ellipsoidal modulation is detected in the photometric r- and i-band light curves, although it is strongly contaminated by flickering activity. By exploiting correlations between the properties of the double-peaked H α emission-line profile and the binary parameters, we derived an orbital inclination of 66.6 ± 4.3 deg, a refined K2 = 562 ± 40 km s-1 and mass ratio q = M2/M1 = 0.07 ± 0.01. From these values, we obtained an updated black hole mass of M1 = 7.8 ± 1.9 M⊙. An independent mass estimate based on X-ray timing agrees well with our value, which gives further support for the outburst quasi-periodic oscillation triplet being explained by the relativistic precession model. We also obtained a companion star mass M2 = 0.55 ± 0.16 M⊙, which is consistent with its K5-K7 V spectral type.