Abstract
We implement, at next-to-next-to-leading order, the QCD corrections to Standard Model Higgs boson production in association with vector bosons at hadron colliders, $q\bar{q} \to HV$ with $V=W,Z$. They consist of the two--loop corrections to the Drell--Yan process for the production of off-shell vector bosons, $q\bar{q} \to V^*$, and in the case of $Z$ final states, of the additional contribution from heavy-quark loop mediated processes, in particular $gg \to HZ$. For the Higgs boson masses relevant at the Tevatron and the LHC, $M_H \lsim 200$--300 GeV, the two-loop corrections are small, increasing the production cross sections by less than 5% and 10%, respectively; the scale dependence is reduced to a level of less than a few per cent. This places these processes among the most theoretically clean Higgs boson production channels at hadron colliders.