The B0 and B+ meson lifetimes have been measured in e+e- annihilation data collected in 1999 and 2000 with the BABAR detector at center-of-mass energies near the Upsilon(4S) resonance. Events are selected in which one B meson is fully reconstructed in a hadronic final state while the second B meson is reconstructed inclusively. A combined fit to the B0 and the B+ decay time difference distributions yields tau_{B0} = 1.546 +/- 0.032 (stat) +/- 0.022(syst) ps, tau_{B+} = 1.673 +/- 0.032 (stat) +/- 0.023 (syst) ps and tau_{B+} / tau_{B0} = 1.082 +/- 0.026 (stat) +/- 0.012 (syst
