We use a large sample of ∼350 000 galaxies constructed by combining the UKIDSS UDS, VIDEO/CFHT-LS, UltraVISTA/COSMOS and GAMA survey regions to probe the major (1:4 stellar mass ratio) merging histories of massive galaxies (>1010 M⊙) at 0.005 < z < 3.5. We use a method adapted from that presented in López-Sanjuan et al., using the full photometric redshift probability distributions, to measure pair fractions of flux-limited, stellar mass selected galaxy samples using close-pair statistics. The pair fraction is found to weakly evolve as ∝ (1 + z)0.8 with no dependence on stellar mass. We subsequently derive major merger rates for galaxies at >1010 M⊙ and at a constant number density of n > 10−4 Mpc−3, and find rates a factor of 2–3 smaller than previous works, although this depends strongly on the assumed merger time-scale and likelihood of a close-pair merging. Galaxies undergo approximately 0.5 major mergers at z < 3.5, accruing an additional (1–4) × 1010 M⊙ in the process. On average, this represents an increase in stellar mass of 20–30 per cent (40–70 per cent) for constant stellar mass (constant number density) samples. Major merger accretion rate densities of ∼2 × 10−4 M⊙ yr−1 Mpc−3 are found for number density selected samples, indicating that direct progenitors of local massive (>1011 M⊙) galaxies have experienced a steady supply of stellar mass via major mergers throughout their evolution. While pair fractions are found to agree with those predicted by the Henriques et al. semi-analytic model, the Illustris hydrodynamical simulation fails to quantitatively reproduce derived merger rates. Furthermore, we find that major mergers become a comparable source of stellar mass growth compared to star formation at z < 1, but is 10–100 times smaller than the star formation rate density at higher redshifts.