The first observation of the Bs0→D̄0K+K- decay is reported, together with the most precise branching fraction measurement of the mode B0→D̄0K+K-. The results are obtained from an analysis of pp collision data corresponding to an integrated luminosity of 3.0 fb-1. The data were collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The branching fraction of the B0→D̄0K+K- decay is measured relative to that of the decay B0→D̄0π+π- to be B(B0→D̄0K+K-)B(B0→D̄0π+π-)=(6.9±0.4±0.3)%, where the first uncertainty is statistical and the second is systematic. The measured branching fraction of the Bs0→D̄0K+K- decay mode relative to that of the corresponding B0 decay is B(Bs0→D̄0K+K-)B(B0→D̄0K+K-)=(93.0±8.9±6.9)%. Using the known branching fraction of B0→D̄0π+π-, the values of B(B0→D̄0K+K-)=(6.1±0.4±0.3±0.3)×10-5 and B(Bs0→D̄0K+K-)=(5.7±0.5±0.4±0.5)×10-5 are obtained, where the third uncertainties arise from the branching fraction of the decay modes B0→D̄0π+π- and B0→D̄0K+K-, respectively.