Electrically induced formation of valley-polarized free-carrier domains is theoretically investigated in two-dimensional (2D) honeycomb lattice systems exhibiting topological valley transport and the valley Hall effect. The results show that under a strong electric field $E$ applied along a nanostrip, the domains can be formed across the strip when this transverse dimension is comparable to the intervalley diffusion length ${L}_{iv}$. Further, these domains are found to be characterized by two distinct length scales dependent on $E$ and ${L}_{iv}$, i.e., the extended diffusion length ${L}_{\mathrm{ext}}$ ($\ensuremath{\propto}{L}_{iv}E$) and the compressed diffusion length ${L}_{\mathrm{com}}$ ($\ensuremath{\propto}{L}_{iv}/E$). The former determines the extension of the domain plateaus, whereas the latter specifies the width of the domain wall. Within each of the domains (excluding a narrow region of the domain wall; ${L}_{\mathrm{ext}}\ensuremath{\gg}{L}_{\mathrm{com}}$), the charge carriers are fully polarized belonging to only one of the valleys, providing a pure bulk valley current inside the considered domain region. The domain properties including the polarization amplitude and domain wall position are analyzed as a function of the applied electric field and intervalley scattering rates at the edges. The position of the domain wall, which determines the relative extension of the plateaus, can be controlled by a transverse current flowing between the Hall-type contacts. The current-voltage characteristic demonstrates a superlinear behavior in the range of electric fields corresponding to the valley-polarization domain formation. This feature is a distinctive signature of the anomalous transport arising from Bloch-band Berry curvature, which enhances the longitudinal conductance and diminishes the channel resistance. By reversing the applied electric field, the valley polarization and localization of the valley-polarized currents can be abruptly switchable. We suggest that the studied scheme of electrically induced domains of valley polarization in the 2D honeycomb lattice systems can be used in novel applications with all-electrical control and manipulation of the valley degree of freedom.