We provide , for the first time , robust observational constraints on the galaxy major merger fraction up to z \approx 6 using spectroscopic close pair counts . Deep Multi Unit Spectroscopic Explorer ( MUSE ) observations in the Hubble Ultra Deep Field ( HUDF ) and Hubble Deep Field South ( HDF-S ) are used to identify 113 secure close pairs of galaxies among a parent sample of 1801 galaxies spread over a large redshift range ( 0.2 < z < 6 ) and stellar masses ( 10 ^ { 7 } -10 ^ { 11 } \mbox { M } _ { \sun } ) , thus probing about 12 Gyr of galaxy evolution . Stellar masses are estimated from spectral energy distribution ( SED ) fitting over the extensive UV-to-NIR HST photometry available in these deep Hubble fields , adding Spitzer IRAC bands to better constrain masses for high-redshift ( z \geqslant 3 ) galaxies . These stellar masses are used to isolate a sample of 54 major close pairs with a galaxy mass ratio limit of 1:6 . Among this sample , 23 pairs are identified at high redshift ( z \geqslant 3 ) through their Ly \alpha emission . The sample of major close pairs is divided into five redshift intervals in order to probe the evolution of the merger fraction with cosmic time . Our estimates are in very good agreement with previous close pair counts with a constant increase of the merger fraction up to z \approx 3 where it reaches a maximum of 20 % . At higher redshift , we show that the fraction slowly decreases down to about 10 % at z \approx 6 . The sample is further divided into two ranges of stellar masses using either a constant separation limit of 10 ^ { 9.5 } \mbox { M } _ { \sun } or the median value of stellar mass computed in each redshift bin . Overall , the major close pair fraction for low-mass and massive galaxies follows the same trend . These new , homogeneous , and robust estimates of the major merger fraction since z \approx 6 are in good agreement with recent predictions of cosmological numerical simulations .