  We calculate radiative corrections to a full set of coupling constants for
the 125 GeV Higgs boson at the one-loop level in two Higgs doublet models with
four types of Yukawa interaction under the softly-broken discrete $Z_2$
symmetry. The renormalization calculations are performed in the on-shell
scheme, in which the gauge dependence in the mixing parameter which appears in
the previous calculation is consistently avoided. We first show the details of
our renormalizaton scheme, and present the complete set of the analytic
formulae of the renormalized couplings. We then numerically demonstrate how the
inner parameters of the model can be extracted by the future precision
measurements of these couplings at the high luminosity LHC and the
International Linear Collider.
