Photonic quantum information processing relies on operating the quantum state of photons, which usually involves bulky optical components unfavorable for system miniaturization and integration. Here, we report on the transformation and distribution of polarization-entangled photon pairs with multichannel dielectric metasurfaces. The entangled photon pairs interact with metasurface building blocks, where the geometrical-scaling-induced phase gradients are imposed, and are transformed into two-photon entangled states with the desired polarization. Two metasurfaces, each simultaneously distributing polarization-entangled photons to spatially separated multiple channels M (N), may accomplish M×N channels of entanglement distribution and transformation. Experimentally we demonstrate 2×2 and 4×4 distributed entanglement states, including Bell states and superposition of Bell states, with high fidelity and strong polarization correlation. We expect this approach paves the way for future integration of quantum information networks.