Revised orbital parameters of the γ2 Velorum system

γ^2 Velorum is the closest and visually brightest Wolf-Rayet (WR) binary system. Its eccentric orbit modulates the X-rays observed from the wind-wind interaction, and its large separation enables spatial resolution of both components. We aim to strengthen the constraints on the properties of γ^2 Velorum and, in particular, to resolve the discrepancy between the eccentricity determined from the emission lines and that from the absorption lines. We obtained VLT/GRAVITY observations and combined them with earlier spatially resolved data covering different orbital phases. We determine strong constraints on all orbital parameters and find that e=0.322, close to the value derived from the emission lines. The X-ray light curve declines as s^-3 after periastron, where s is the separation of the two stars, but its modulation is likely affected by absorption and occultation of the X-ray emitting region at other orbital phases. We find that previous discrepancies in the reddening value can be traced to a brighter K-band magnitude than predicted by the WR wind models. We derive E(B-V)=0.02± 0.02,mag. Our more precise mass and radius values, combined with previously determined effective temperatures, provide strong constraints on evolutionary models. The closest match for the O star comes from a rotationally mixed model with initial mass M_ =28.7, _⊙ and an M_ =32, _⊙ model for the WR star, with negligible accretion onto the O star during the WR progenitor's Roche lobe overflow phase. However, the temperature of the O star is higher and the mass of the WR star is smaller than predicted by the evolutionary tracks at the current epoch, consistent with the well-known ``mass-discrepancy problem'' in massive stars. init M init M γ^2 Velorum's strongly constrained parameters make it ideal for testing structure, evolution, and stellar wind models.