The decay-time-dependent CP asymmetry in B_{s}^{0}→J/ψ(→μ^{+}μ^{-})K^{+}K^{-} decays is measured using proton-proton collision data, corresponding to an integrated luminosity of 6 fb^{-1}, collected with the LHCb detector at a center-of-mass energy of 13 TeV. Using a sample of approximately 349 000 B_{s}^{0} signal decays with an invariant K^{+}K^{-} mass in the vicinity of the ϕ(1020) resonance, the CP-violating phase ϕ_{s} is measured, along with the difference in decay widths of the light and heavy mass eigenstates of the B_{s}^{0}-B[over ¯]_{s}^{0} system, ΔΓ_{s}, and the difference of the average B_{s}^{0} and B^{0} meson decay widths, Γ_{s}-Γ_{d}. The values obtained are ϕ_{s}=-0.039±0.022±0.006 rad, ΔΓ_{s}=0.0845±0.0044±0.0024 ps^{-1}, and Γ_{s}-Γ_{d}=-0.0056_{-0.0015}^{+0.0013}±0.0014 ps^{-1}, where the first uncertainty is statistical and the second systematic. These are the most precise single measurements to date and are consistent with expectations based on the Standard Model and with the previous LHCb analyses of this decay. These results are combined with previous independent LHCb measurements. The phase ϕ_{s} is also measured independently for each polarization state of the K^{+}K^{-} system and shows no evidence for polarization dependence.