We present a measurement of the top-quark pair production cross section in proton-antiproton collisions at s√=1.96 TeV. The data were collected at the Fermilab Tevatron by the CDF II detector and correspond to an integrated luminosity of 8.8 fb−1, representing the complete CDF Run II data set. We select events consistent with the production of top-quark pairs by requiring the presence of two reconstructed leptons, an imbalance in the total event transverse momentum, and jets. At least one jet is required to be identified as consistent with the fragmentation of a bottom quark using a secondary-vertex-finding algorithm. The 246 candidate events are estimated to have a signal purity of 91%. We measure a cross section of σtt¯=7.09±0.84 pb, assuming a top-quark mass of 172.5 GeV/c2. The results are consistent with the standard model as predicted by next-to-leading-order calculations.