I will present the computation of the next-to-leading order (NLO) QCD corrections to electroweak Higgs plus three jet production (EW H+3jets) within the Matchbox NLO framework of the Herwig++ event generator. Both vector boson fusion (VBF) and Higgs-strahlung type contributions are included along with all interferences. I will discuss features of our Matchbox implementation and show the impact of QCD corrections on kinematic distributions relevant Higgs boson studies at the CERN Large Hadron Collider (LHC).