This research introduces an integrated vibration energy harvester and electrochemical energy storage device that can effectively convert ambient vibrations directly into stored electrochemical energy. The electrochemical energy storage device is an electrical double layer capacitor (EDLC) with an ionic redox transistor as its membrane separator. This 'smart' membrane separator directly rectifies the electrical energy generated by the transduction from the nonlinear energy harvester, creating an ionic polarization across the membrane separator for storage. This electrochemical gradient can be subsequently used for powering sensor electronics as required in various applications, including structural condition monitoring. The alternating voltage developed by the energy harvester (+/- 5V around 100 Hz) is connected to an aqueous supercapacitor fabricated from nanofibrous carbon paper electrodes and a polypyrrole-based (PPy(DBS)) smart membrane separator. A potential below -400mV from the energy harvester applied to the supercapacitor turns the smart membrane separator 'ON' and results in a unidirectional ionic current of Li+ ions. As the potential developed by the harvester cycles above ∼50 mV, the membrane separator switches 'OFF' and prevents the discharge of the rectified current. This leads to a continuous polarization of ions towards electrical fields relevant for powering electronics. This article is the first description and demonstration of an energy harvesting and storage system that can directly convert the electrical energy from a vibration energy harvester into electrochemical energy without the use of passive circuit components for power rectification.