We investigate the inclusive Higgs boson production in proton–proton collisions at high energies in the framework of kT-factorization QCD approach. The attention is focused on the dominant off-shell gluon–gluon fusion subprocess g⁎g⁎→H→γγ, where the transverse momentum of incoming gluons are taken into account. The transverse momentum dependent (or unintegrated) gluon densities of the proton are determined using the CCFM evolution equation as well as the Kimber–Martin–Ryskin prescription. We study the theoretical uncertainties of our calculations and perform the comparison with the results of traditional pQCD evaluations. Our predictions agree well with the first experimental data taken by the ATLAS Collaboration at the LHC. We argue that further studies of the Higgs boson production are capable of constraining the unintegrated gluon densities of the proton.