Quantum teleportation is a fundamental concept in quantum physics that now finds important applications at the heart of quantum technology, including quantum relays, quantum repeaters and linear optics quantum computing. Photonic implementations have largely focused on achieving long-distance teleportation for decoherence-free quantum communication. Teleportation also plays a vital role in photonic quantum computing, for which large linear optical networks will probably require an integrated architecture. Here, we report a fully integrated implementation of quantum teleportation in which all key parts of the circuit—entangled state preparation, Bell-state analysis and tomographic state measurement—are performed on a reconfigurable photonic chip. We also show that a novel element-wise characterization method is critical to the mitigation of component errors, a key technique that will become increasingly important as integrated circuits reach the higher complexities necessary for quantum enhanced operation.