A search for the B0→K+K− decay is performed using pp-collision data collected by LHCb. The data set corresponds to integrated luminosities of 1.0 and 2.0 fb−1 at center-of-mass energies of 7 and 8 TeV, respectively. This decay is observed for the first time, with a significance of more than 5 standard deviations. The analysis also results in an improved measurement of the branching fraction for the Bs0→π+π− decay. The measured branching fractions are B(B0→K+K−)=(7.80±1.27±0.81±0.21)×10−8 and B(Bs0→π+π−)=(6.91±0.54±0.63±0.19±0.40)×10−7. The first uncertainty is statistical, the second is systematic, the third is due to the uncertainty on the B0→K+π− branching fraction used as a normalization. For the Bs0 mode, the fourth accounts for the uncertainty on the ratio of the probabilities for b quarks to hadronize into Bs0 and B0 mesons.Received 27 October 2016DOI:https://doi.org/10.1103/PhysRevLett.118.081801Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.© 2017 CERN, for the LHCb CollaborationPhysics Subject Headings (PhySH)Research AreasFlavor changing neutral currentsHadronic decaysPhysical SystemsBottom mesonsTechniquesArtificial neural networksCherenkov detectorsHadron collidersParticles & Fields