  We compute the factorising second-order QCD corrections to the electroweak
production of a Higgs boson through vector boson fusion. Our calculation is
fully differential in the kinematics of the Higgs boson and of the final state
jets, and uses the antenna subtraction method to handle infrared singular
configurations in the different parton-level contributions. Our results allow
us to reassess the impact of the next-to-leading order (NLO) QCD corrections to
electroweak Higgs-plus-three-jet production and of the next-to-next-to-leading
order (NNLO) QCD corrections to electroweak Higgs-plus-two-jet production. The
NNLO corrections are found to be limited in magnitude to around $\pm 5\%$ and
are uniform in several of the kinematical variables, displaying a kinematical
dependence only in the transverse momenta and rapidity separation of the two
tagging jets.
