Self-healing materials are indispensable for soft actuators and robots that operate in dynamic and real-world environments, as these machines are vulnerable to mechanical damage. However, current self-healing materials have shortcomings that limit their practical application, such as low healing strength (below a megapascal) and long healing times (hours). Here, we introduce high-strength synthetic proteins that self-heal micro- and macro-scale mechanical damage within a second by local heating. These materials are optimized systematically to improve their hydrogen-bonded nanostructure and network morphology, with programmable healing properties (2-23 MPa strength after 1 s of healing) that surpass by several orders of magnitude those of other natural and synthetic soft materials. Such healing performance creates new opportunities for bioinspired materials design, and addresses current limitations in self-healing materials for soft robotics and personal protective equipment.