  The recent discovery of a new boson of mass roughly 125 GeV has been reported
by the ATLAS and CMS collaborations. Although its signals in various decay
modes resemble those of the standard model (SM) Higgs boson, observed are the
combinations of entangled information about the production, decay rates and
total decay width of the new boson. In addition, some decay channels show
non-negligible deviation from the SM expectation, such as the $2\sigma$ excess
in the diphoton channel. In the four types (I, II, X and Y) of two Higgs
doublet models, we perform the global $\chi^2$ fit in three scenarios: (i) the
new boson is the light CP-even Higgs boson $h^0$; (ii) it is the heavy CP-even
Higgs boson $H^0$; (iii) the signals are from degenerate $h^0$ and the
pseudoscalar $A^0$. Considering other phenomenological constraints such as
flavor physics, electroweak precision data, and the LEP search for the Higgs
boson, we find that the the first scenarios in Type II and Type Y models
actually provide better or similarly good fit to the data than the SM. All the
other models are excluded at 95% C.L..
