Abstract: The decays B-c(+) -> J/ psi D-s(+) and B-c(+) -> J/ psi D-s*(+) are observed for the first time using a dataset, corresponding to an integrated luminosity of 3 fb(-1), collected by the LHCb experiment in proton-proton collisions at center-of-mass energies of root s = 7 and 8 TeV. The statistical significance for both signals is in excess of 9 standard deviations. The following ratios of branching fractions are measured to be 'B(B-c(+) -> J/ psi D-s(+))/B(B-c(+) -> J/ psi pi(+)) = 2.90 +/- 0.57 +/- 0.24, B(B-c(+) -> J/psi D-s*(+))/B(B-c(+) -> J/ psi D-s(+)) = 2.37 +/- 0.56 +/- 0.10, where the first uncertainties are statistical and the second systematic. The mass of the B-c(+) meson is measured to be m(Bc+) = 6276.28 +/- 1.44(stat) +/- 0.36(syst) MeV/c(2), using the B-c(+) -> J/ psi D-s(+) decay mode.