Using pp collision data corresponding to an integrated luminosity of 1.0 fb(-1) and collected by LHCb in 2011 at a center-of-mass energy of 7 TeV, we report the measurement of direct CP violation in B(s)(0)→K(-)π(+) decays, A(CP)(B(s)(0)→K(-)π(+)=0.27±0.04 (stat)±0.01 (syst), with significance exceeding 5 standard deviations. This is the first observation of CP violation in the decays of B(s)(0) mesons. Furthermore, we provide an improved determination of direct CP violation in B(0)→K(+)π(-) decays, A(CP)(B(0)→K(+)π(-)=-0.080±0.007 (stat)±0.003 (syst), which is the most precise measurement of this quantity to date.