We report a measurement of the time-dependent CP asymmetry of B[over ¯]^{0}→D_{CP}^{(*)}h^{0} decays, where the light neutral hadron h^{0} is a π^{0}, η, or ω meson, and the neutral D meson is reconstructed in the CP eigenstates K^{+}K^{-}, K_{S}^{0}π^{0}, or K_{S}^{0}ω. The measurement is performed combining the final data samples collected at the ϒ(4S) resonance by the BABAR and Belle experiments at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively. The data samples contain (471±3)×10^{6} BB[over ¯] pairs recorded by the BABAR detector and (772±11)×10^{6} BB[over ¯] pairs recorded by the Belle detector. We measure the CP asymmetry parameters -η_{f}S=+0.66±0.10(stat)±0.06(syst) and C=-0.02±0.07(stat)±0.03(syst). These results correspond to the first observation of CP violation in B[over ¯]^{0}→D_{CP}^{(*)}h^{0} decays. The hypothesis of no mixing-induced CP violation is excluded in these decays at the level of 5.4 standard deviations.