We present a combined measurement of the Cabibbo-Kobayashi-Maskawa matrix element | V c b | and of the parameters ρ 2 , R 1 ( 1 ) , and R 2 ( 1 ) , which fully characterize the form factors for the B 0 → D * − ℓ + ν ℓ decay in the framework of heavy-quark effective field theory. The results, based on a selected sample of about 52 800 B 0 → D * − ℓ + ν ℓ decays, recorded by the BABAR detector, are ρ 2 = 1.157 ± 0.094 ± 0.027 , R 1 ( 1 ) = 1.327 ± 0.131 ± 0.043 , R 2 ( 1 ) = 0.859 ± 0.077 ± 0.021 , and F ( 1 ) | V c b | = ( 34.7 ± 0.4 ± 1.0 ) × 10 − 3 . The first error is the statistical and the second is the systematic uncertainty. Combining these measurements with the previous BABAR measurement of the form factors, which employs a different fit technique on a partial sample of the data, we improve the statistical precision of the result, ρ 2 = 1.191 ± 0.048 ± 0.028 , R 1 ( 1 ) = 1.429 ± 0.061 ± 0.044 , R 2 ( 1 ) = 0.827 ± 0.038 ± 0.022 , and F ( 1 ) | V c b | = ( 34.4 ± 0.3 ± 1.1 ) × 10 − 3 . Using lattice calculations for the axial form factor F ( 1 ) , we extract | V c b | = ( 37.4 ± 0.3 ± 1.2 ± 1.2 1.4 ) × 10 − 3 , where the third error is due to the uncertainty in F ( 1 ) . We also present a measurement of the exclusive branching fraction, B = ( 4.69 ± 0.04 ± 0.34 ) % .