The CP violation observables S and C in the decay channel B^{0}→D^{+}D^{-} are determined from a sample of proton-proton collisions at center-of-mass energies of 7 and 8 TeV, collected by the LHCb experiment and corresponding to an integrated luminosity of 3 fb^{-1}. The observable S describes CP violation in the interference between mixing and the decay amplitude, and C parametrizes direct CP violation in the decay. The following values are obtained from a flavor-tagged, decay-time-dependent analysis: S=-0.54_{-0.16}^{+0.17}(stat)±0.05(syst), C=0.26_{-0.17}^{+0.18}(stat)±0.02(syst). These values provide evidence for CP violation at a significance level of 4.0 standard deviations. The phase shift due to higher-order standard model corrections is constrained to a small value of Δϕ=-0.16_{-0.21}^{+0.19} rad.