Context. The mass assembly of galaxies can proceed through different physical processes. Here we report on the spectroscopic identification of close physical pairs of galaxies at redshifts 2 less than or similar to z < 4 and discuss the impact of major mergers in building galaxies at these early cosmological times. Aims. We aim to identify and characterize close physical pairs of galaxies destined to merge and use their properties to infer the contribution of merging processes to the early mass assembly of galaxies. Methods. We searched for galaxy pairs with a transverse separation r(p) <= 25 h(-1) kpc and a velocity difference Delta(v) <= 500 km s(-1) using early data from the VIMOS Ultra Deep Survey (VUDS) that comprise a sample of 1111 galaxies with spectroscopic redshifts measurements at redshifts 1.8 <= z <= 4 in the COSMOS. ECDFS, and VVDS-02h fields, combined with VVDS data. We analysed their spectra and associated visible and near-infrared photometry to assess the main properties of merging galaxies that have an average stellar mass M-* = 2.3 x 10(10) M-circle dot at these redshifts. Results. Using the 12 physical pairs found in our sample we obtain a first robust measurement of the major merger fraction at these redshifts, f(MM)= 19.4(-6)(+9)%. These pairs are expected to merge within 1 Gyr on average each producing a more massive galaxy by the time the cosmic star formation peaks at z similar to 1-2. Using the pairs' merging time scales, we derive a merging rate of R-MM = 0.17(-0.05)(+0.08) Gyr(-1). From the average mass ratio between galaxies in the pairs, the stellar mass of the resulting galaxy after merging will be similar to 60% higher than the most massive galaxy in the pair before merging. We conclude that major merging of galaxy pairs is on-going at 2 less than or similar to z < 4 and is significantly contributing to the major mass assembly phase of galaxies at this early epoch.