The first measurement of the effective lifetime of the B(s)(0) meson in the decay B(s)(0) → 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 B(s)(0) → 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 B(s)(0) mass eigenstate of ΓL = 0.725 ± 0.014 ± 0.009 ps(-1). The B(s)(0) lifetime is also measured using the flavor-specific B(s)(0)→ D-Ds+ decay to be 1.52 ± 0.15 ± 0.01 ps.