We present the complete two-loop electroweak corrections to $gg\to H$, the main partonic channel for the production of the Higgs boson at hadron colliders. The evaluation is based on a numerical approach and the result covers all kinematical regions, including $WW$ and $ZZ$ thresholds, by introducing complex masses for the $W$ and the $Z$ bosons. Furthermore the relation between physical observables measured at LHC and Tevatron and Higgs pseudo-observables (production cross section
and partial decay widths) is revised by extensively using the notion of the Higgs complex pole. Numerical effects for the Higgs production cross section are presented.