We report the observation of decays B{0}-->D{s}{(*)+}pi- and B{0}-->D{s}{(*)-}K+ in a sample of 230 x 10(6) Upsilon(4S)-->BB[over] events recorded with the BABAR detector at the SLAC PEP-II asymmetric-energy e+ e- storage ring. We measure the branching fractions B(B{0}-->D{s}{+}pi-)=(1.3+/-0.3(stat)+/-0.2(syst))x10(-5), B(B{0}-->D{s}{-} K+)=(2.5+/-0.4(stat)+/-0.4(syst))x10(-5), B(B{0}-->D{s}{*+}pi-)=(2.8+/-0.6(stat)+/-0.5(syst))x10(-5), and B(B{0}-->D{s}{*-}K+)=(2.0+/-0.5(stat)+/-0.4(syst))x10(-5). The significances of the measurements to differ from zero are 5, 9, 6, and 5 standard deviations, respectively. This is the first observation of B{0}-->D{s}{+}pi-, B{0}-->D{s}{*+}pi-, and B{0}-->D{s}{*-}K+ decays.