The age of a young asteroid family can be determined by tracking the orbits of family members backward in time and showing that they converge at some time in the past. Here we consider the Veritas family. We find that the membership of the Veritas family increased enormously since the last detailed analysis of the family. Using backward integration, we confirm the convergence of nodal longitudes {Omega}, and, for the first time, also obtain a simultaneous convergence of pericenter longitudes {varpi}. The Veritas family is found to be 8.23^+0.37^-0.31_Myr old. To obtain a tight convergence of {Omega} and {varpi}, as expected from low ejection speeds of fragments, the Yarkovsky effect needs to be included in the modeling of the past orbital histories of Veritas family members. Using this method, we compute the Yarkovsky semi-major axis drift rates, d_a/dt, for 274 member asteroids. The distribution of d_a_/dt values is consistent with a population of C-type objects with low densities and low thermal conductivities. The accuracy of individual d_a_/dt measurements is limited by the effect of close encounters of member asteroids to (1) Ceres and other massive asteroids, which cannot be evaluated with confidence.