We report the results of a study of the exclusive semileptonic decays B-→π0ℓ-ν̅ ℓ, B̅ 0→π+ℓ-ν̅ ℓ, B-→ρ0ℓ-ν̅ ℓ, B̅ 0→ρ+ℓ-ν̅ ℓ and B-→ωℓ-ν̅ ℓ, where ℓ represents an electron or a muon. The events are tagged by fully reconstructing a second B meson in the event in a hadronic decay mode. The measured branching fractions are B(B-→π0ℓ-ν̅ ℓ)=(0.80±0.08±0.04)×10-4, B(B̅ 0→π+ℓ-ν̅ ℓ)=(1.49±0.09±0.07)×10-4, B(B-→ρ0ℓ-ν̅ ℓ)=(1.83±0.10±0.10)×10-4, B(B̅ 0→ρ+ℓ-ν̅ ℓ)=(3.22±0.27±0.24)×10-4, and B(B-→ωℓ-ν̅ ℓ)=(1.07±0.16±0.07)×10-4, where the first error is statistical and the second one is systematic. The obtained branching fractions are inclusive of soft photon emission. We also determine the branching fractions as a function of the 4-momentum transfer squared to the leptonic system q2=(pℓ+pν)2, where pℓ and pν are the lepton and neutrino 4-momenta, respectively. Using the pion modes, a recent light cone sum rule calculation, lattice QCD results and a model-independent description of the hadronic form factor, a value of the Cabibbo-Kobayashi-Maskawa matrix element Vub =(3.52±0.29)×10-3 is extracted. A structure in the two-pion invariant mass distribution near 1.3 GeV/c2, which might be dominated by the decay B-→f2(1270)ℓ-ν̅ ℓ, f2→π+π-, is seen. These results are obtained from a 711 fb-1 data sample that contains 772×106 BB̅ pairs, collected near the Υ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider.