The controllable modulation of carrier polarity in semiconductors is essential for enabling dynamic configurations in reconfigurable devices. Ambipolar two-dimensional (2D) semiconductors, characterized by their atomic-scale thickness and excellent gate modulation efficiency, have emerged as highly promising channel materials for such devices. However, existing methods for polarity control encounter challenges in achieving reversible modulation during device operation. Here, we report a novel strategy for reversibly modulating the polarity of ambipolar 2D semiconductors through gate-controlled charge trapping. We demonstrate a double-gate TaOx/WSe2/h-BN field-effect transistor, which can reversibly switch between n-type and p-type transport characteristics via electric-field-driven bipolar charge trapping at the TaOx/WSe2 interface. With this method, an electrically configurable complementary inverter is created with a single WSe2 flake, exhibiting a power consumption of just 0.7 nW. Additionally, a programmable p-n/n-p diode is realized with a > 100,000-fold change in the rectification ratio. These results demonstrate the great potential of gate-controlled bipolar charge trapping for advancing reconfigurable electronics.