We compute in the heavy-quark effective theory the two-loop anomalous dimension of the effective four-fermion operator whose matrix element determines the B-parameter of the B-meson. Dimensional reduction is the regularization method chosen in this calculation, which is performed using the techniques already developed by us to treat the two-loop renormalization in standard dimensional regularization of the heavy-quark axial current. For N = 3, we find , with . This anomalous dimension turns out to be equal to the one in standard dimensional regularization. We employ to derive the complete scheme-independent order α_s correction to therelation between O_{ΔB = 2} in QCD and its counterpart in the effective theory. For the heavy-quark axial current, we recalculate the corresponding analogous order-α_s relation in dimensional reduction and the 't Hooft-Veltman dimensional regularization scheme. We show explicitly that this is renormalization-scheme independent, which completes the study carried out by us in our previous work. Moreover, these relations are used to obtain the renormalization constants for the lattice values of the B-meson decay constant, ƒ_B, and B-parameter, B_B, whose product enters the theoretical prediction of the mixing. As an extra result, the theoretic subtleties of dimensional reduction applied to the heavy-quark effective theory are exposed and resolved.