We compute the cross section and differential distributions for the production of a Standard Model Higgs boson in association with a hadronic jet to next-to-next-to-leading order in quantum chromodynamics (QCD). In Higgs boson studies at the LHC, final states containing one jet are a dominant contribution to the total event rate, and their understanding is crucial for improved determinations of the Higgs boson properties. We observe substantial higher order corrections to transverse momentum

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... ctra and rapidity distributions in Higgs-plus-one-jet final states. Their inclusion stabilises the residual theoretical uncertainty of the predictions around 9%, thereby providing important input to precision studies of the Higgs boson.