The result of a search for the decay Bc+→Bs0π+ is presented, using the Bs0→Ds-π+ and Bs0→J/ψ channels. The analysis is based on a data sample of pp collisions collected with the LHCb detector, corresponding to an integrated luminosity of 1 fb-1 taken at a center-of-mass energy of 7 TeV, and 2 fb-1 taken at 8 TeV. The decay Bc+→Bs0π+ is observed with significance in excess of 5 standard deviations independently in both decay channels. The measured product of the ratio of cross sections and branching fraction is [σ(Bc+)/ σ(Bs0)]×B(Bc+→Bs0π+)=[2.37±0.31 (stat)±0.11 (syst)-0.13+0.17(τBc+)]×10-3, in the pseudorapidity range 2<η(B)<5, where the first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty on the Bc+ lifetime. This is the first observation of a B meson decaying to another B meson via the weak interaction. © 2013 CERN. Published by the American Physical Society.