The direct imaging of exoplanet is a leading field of today’s astronomy. The photons coming from the planet carry precious information on the chemical composition of its atmosphere. The second-generation instrument, Spectro-Polarimetric High contrast Exoplanet Research (SPHERE), dedicated to detection, photometry and spectral characterization of Jovian-like planets, is now in operation on the European very large telescope. This instrument relies on an extreme adaptive optics (XAO) system to compensate for atmospheric turbulence as well as for internal errors with an unprecedented accuracy. We demonstrate the high level of performance reached by the SPHERE XAO system (SAXO) during the assembly integration and test (AIT) period. In order to fully characterize the instrument quality, two AIT periods have been mandatory. In the first phase at Observatoire de Paris, the performance of SAXO itself was assessed. In the second phase at IPAG Grenoble Observatory, the operation of SAXO in interaction with the overall instrument has been optimized. In addition to the first two phases, a final check has been performed after the reintegration of the instrument at Paranal Observatory, in the New Integration Hall before integration at the telescope focus. The final performance aimed by the SPHERE instrument with the help of SAXO is among the highest Strehl ratio pretended for an operational instrument (90% in H band, 43% in V band in a realistic turbulence r0, and wind speed condition), a limit R magnitude for loop closure at 15, and a robustness to high wind speeds. The full-width at half-maximum reached by the instrument is 40 mas for infrared in H band and unprecedented 18.5 mas in V band.