Electric control of magnetic vortex dynamics in a reproducible way on an ultrafast time scale is crucial for efficient, low-energy spintronic devices. This study demonstrates a novel packaged-skyrmion-mediated vortex switching process driven by picosecond electrical field pulses via magnetoelectric interactions. Both vortex chirality and polarity show well-defined reversal behavior, enabling repeated switching between four magnetic vortex states. This provides an energy-efficient, highly localized, and coherent control method for nonvolatile magnetic vortex-based information storage and handling.