The tau lepton lifetime has been measured with the e+e- -> tau+tau- events collected by the DELPHI detector at LEP in the years 1991-1995. Three different methods have been exploited, using both one-prong and three-prong tau decay channels. Two measurements have been made using events in which both taus decay to a single charged particle. Combining these measurements gave tau_tau (1 prong) = 291.8 +/- 2.3 (stat) +/- 1.5 (sys) fs. A third measurement using taus which decayed to three charged particles yielded tau_tau (3 prong) = 288.6 +/- 2.4 (stat) +/- 1.3 (sys) fs. These were combined with previous DELPHI results to measure the tau lifetime, using the full LEP1 data sample, to be tau_tau = 290.9 +/- 1.4 (stat) +/- 1.0 (sys) fs.