  We present a computation of the cross section for inclusive Higgs production
in gluon-gluon fusion for finite values of the top mass in perturbative QCD to
all orders in the limit of high partonic center-of-mass energy. We show that at
NLO the high energy contribution accounts for most of the difference between
the result found with finite top mass and that obtained in the limit of
infinite top mass. We use our result to improve the known NNLO order result
obtained with infinite top mass. We estimate the effect of the high energy NNLO
top mass dependence on the K factor to be of the order of a few per cent.
