Photon entanglement is an important state of light that is at the basis of many protocols in photonic quantum technologies, from quantum computing, to simulation and sensing. The capability to generate entangled photons in integrated waveguide sources is particularly advantageous due to the enhanced stability and more efficient light-crystal interaction. Here we realize an integrated optical source of entangled degenerate photons at telecom wavelength, based on the hybrid interfacing of photonic circuits in different materials, all inscribed by femtosecond laser pulses. We show that our source, based on spontaneous parametric down-conversion, gives access to different classes of output states, allowing to switch from path-entangled to polarization-entangled states with net visibilities above 0.92 for all selected combinations of integrated devices. * These authors contributed equally. †