© 2015, The Author(s). Abstract: A study of B and Bs meson decays into J/ψ η and J/ψ η′ final states is performed using a data set of proton-proton collisions at centre-of-mass energies of 7 and 8 TeV, collected by the LCHb experiment and corresponding to 3.0 fb−1 of integrated luminosity. The decay B0 → J/ψ η′ is observed for the first time. The following ratios of branching fractions are measured: (Formula Presented) where the third uncertainty is related to the present knowledge of fs/fd, the ratio between the probabilities for a b quark to form a Bs or a B0 meson. The branching fraction ratios are used to determine the parameters of η − η′ meson mixing. In addition, the first evidence for the decay Bs → ψ(2S)η′ is reported, and the relative branching fraction is measured, (Formula Presented) where the third uncertainty is due to the limited knowledge of the branching fractions of J/ψ and ψ(2S) mesons.