  We compute the next-to-next-to-leading order QCD corrections to Higgs boson
production in weak boson fusion followed by its decay to a $b\bar b$ pair or to
a pair of leptonically-decaying $W$ bosons. Our calculation allows us to
compute realistic fiducial cross sections and assess the impact of fiducial
cuts applied to the Higgs boson decay products on the magnitude of QCD
radiative corrections in weak boson fusion.
