The first measurement of the effective lifetime of the B̄s0 meson in the decay B̄s0→Ds-Ds+ is reported using a proton-proton collision data set, corresponding to an integrated luminosity of 3 fb-1, collected by the LHCb experiment. The measured value of the B̄s0→Ds-Ds+ effective lifetime is 1.379±0.026±0.017 ps, where the uncertainties are statistical and systematic, respectively. This lifetime translates into a measurement of the decay width of the light B̄s0 mass eigenstate of ΓL=0.725±0. 014±0.009 ps-1. The B̄s0 lifetime is also measured using the flavor-specific B̄s0→D-Ds+ decay to be 1.52±0.15±0.01 ps.