We consider Standard Model Higgs boson production in association with a Z boson in hadron collisions. We present a fully exclusive computation of QCD radiative corrections up to next-to-next-to-leading order (NNLO). Our calculation includes the Higgs boson decay to bottom quarks (b) in next-to-leading order QCD and the leptonic decay of the Z boson with finite-width effects and spin correlations. The computation is implemented in a parton level Monte Carlo program that makes possible to consider arbitrary kinematical cuts on the final-state leptons, the b jets and the associated QCD radiation, and to compute the corresponding distributions in the form of bin histograms. We assess the impact of QCD radiative effects in the boosted kinematics at the LHC and show that the inclusion of the NNLO corrections is crucial to control the pT spectrum of the Higgs boson candidate.