A bstract We present calculations of Higgs boson production via gluon-gluon fusion in association with one or two additional jets at next-to-leading order in QCD. The calculation of H +jet is exact in the treatment of the top-quark mass, whereas for the H +2 jets calculation the two-loop virtual amplitudes are approximated via a reweighting with leading-order mass effects, while keeping all top-quark mass effects in the real radiation contributions. For H +jet production, this study extends a previous calculation, revealing an error in the previous results. For total and differential cross sections, we present new results and compare the QCD corrections with the infinite top-mass limit, for which we find a strikingly good agreement if all amplitudes are rescaled by the leading-order mass dependence.