We present a measurement of the Cabibbo-Kobayashi-Maskawa matrix element /Vub/, based on 253 fb(-1) of data collected by the Belle detector at the KEKB e+ e- asymmetric collider. Events are tagged by fully reconstructing one of the B mesons, produced in pairs from Gamma(4S). The signal for b --> u semileptonic decay is distinguished from the b --> c background using the hadronic mass Mx, the leptonic invariant mass squared q2 and the variable P+ [triple bond] Ex - /px/. The results are obtained for events with p(l)* > or = 1 GeV/c, in three kinematic regions (1) Mx < 1.7 GeV/c2, (2) Mx < 1.7 GeV/c2 combined with q2 > 8 GeV2/c2, and by (3) P+ < 0.66 GeV/c. The matrix element /Vub/ is found to be (4.09 +/- 0.19 +/- 0.20(+0.14) -0.15 +/- 0.18) x 10(-3), where the errors are statistical, systematic including Monte Carlo modeling, theoretical, and from shape function parameter determination, respectively.