Electrode arrays that interface with peripheral nerves are used in the diagnosis and treatment of neurological disorders; however, they require complex placement surgeries that carry a high risk of nerve injury. Here we leverage recent advances in soft robotic actuators and flexible electronics to develop highly conformable nerve cuffs that combine electrochemically driven conducting-polymer-based soft actuators with low-impedance microelectrodes. Driven with applied voltages as small as a few hundreds of millivolts, these cuffs allow active grasping or wrapping around delicate nerves. We validate this technology using in vivo rat models, showing that the cuffs form and maintain a self-closing and reliable bioelectronic interface with the sciatic nerve of rats without the use of surgical sutures or glues. This seamless integration of soft electrochemical actuators with neurotechnology offers a path towards minimally invasive intraoperative monitoring of nerve activity and high-quality bioelectronic interfaces.