A consequent tendency toward high-performance quantum information processing is to develop the fully integrated photonic chip. Here, we report the on-chip generation and manipulation of entangled photons based on reconfigurable lithium-niobate waveguide circuits. By introducing a periodically poled structure into the waveguide circuits, two individual photon-pair sources with a controllable electro-optic phase shift are produced within a Hong-Ou-Mandel interferometer, resulting in a deterministically separated identical photon pair. The state is characterized by 92.9±0.9% visibility Hong-Ou-Mandel interference. The photon flux reaches ∼1.4×10(7)  pairs nm-1 mW-1. The whole chip is designed to contain nine similar units to produce identical photon pairs spanning the telecom C and L band by the flexible engineering of nonlinearity. Our work presents a scenario for on-chip engineering of different photon sources and paves the way to fully integrated quantum technologies.