Using p p 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 C P violation in B 0 s → K − π + decays, A C P ( B 0 s → K − π + ) = 0.27 ± 0.04   ( stat ) ± 0.01   ( syst ) , with significance exceeding 5 standard deviations. This is the first observation of C P violation in the decays of B 0 s mesons. Furthermore, we provide an improved determination of direct C P violation in B 0 → K + π − decays, A C P ( B 0 → K + π − ) = − 0.080 ± 0.007   ( stat ) ± 0.003   ( syst ) , which is the most precise measurement of this quantity to date.