Résumé : The bb̄ forward-backward asymmetry has been determined from the average charge flow measured in a sample of 3,500,000 hadronic Z decays collected with the DELPHI detector in 1992 - 1995. The measurement is performed in an enriched bb̄ sample selected using an impact parameter tag and results in the following values for the bb̄ forward-backward asymmetry: Abb̄FB (89.55 GeV) = 0.068 ± 0.018 (stat.) ± 0.0013(syst.) Abb̄FB (91.26 GeV) = 0.0982 ± 0.0047(stat.) ± 0.0016(syst.) Abb̄FB (92.94 GeV) = 0.123 ± 0.016 (stat.) ± 0.0027(syst.) The bb̄ charge separation required for this analysis is directly measured in the b tagged sample, while the other charge separations are obtained from a fragmentation model precisely calibrated to data. The effective weak mixing angle is deduced from the measurement to be: sin2θ1eff = 0.23186 ± 0.00083.