We present the calculation of the NLO QCD corrections to the associated production of a Higgs boson and two jets, in the infinite top-mass limit. We discuss the technical details of the computation and we show the numerical impact of the radiative corrections on several observables at the LHC. The results are obtained by using a fully automated framework for fixed order NLO QCD calculations based on the interplay of the packages GoSam and Sherpa. The evaluation of the virtual corrections constitutes an application of the d-dimensional integrand-level reduction to theories with higher dimensional operators. We also present first results for the one-loop matrix elements of the partonic processes with a quark-pair in the final state, which enter the hadronic production of a Higgs boson together with three jets in the infinite top-mass approximation.