  We compute the total cross-section for direct Higgs boson production in
hadron collisions at NNLO in perturbative QCD. A new technique which allows us
to perform an algorithmic evaluation of inclusive phase-space integrals is
introduced, based on the Cutkosky rules, integration by parts and the
differential equation method for computing master integrals. Finally, we
discuss the numerical impact of the O(alpha_s^2) QCD corrections to the Higgs
boson production cross-section at the LHC and the Tevatron.
